multitiered nonlinear morphology using multitape finite...

Multitiered Nonlinear Morphology UsingMultitape Finite Automata A Case Studyon Syriac and Arabic

George Anton KirazBell Laboratories Lucent Technologies

He who corrects the alphabetical ordering [of this Lexicon] does nottake into account the letters which are added or those that changehere and there due to inexion at the beginning of the lexis [ieword] but goes back to the base form of the word

ndash Abu H asan Bar Bahlul ( ca 963)Syriac Lexicon Duvalrsquos edition (Paris 1888)

This paper presents a computational model for nonlinear morphology with illustrations fromSyriac and Arabic The model is a multitiered one in that it allows for multiple lexical representa-tions corresponding to the multiple tiers of autosegmental phonology The model consists of threemain components (i) a lexicon which is made of sublexica with each sublexicon representinglexical material from a specic tier (ii) a rewrite rules component that maps multiple lexicalrepresentations into one surface form and vice versa and (iii) a morphotactic component thatemploys regular grammars The system is nite-state in that lexica and rules can be representedby multitape nite-state machines

1 Introduction

This paper is concerned with presenting a general nite-state framework for comput-ing complex nonlinear (ie nonconcatenative) morphophonological descriptions Theframework subsumes previous models in that it is not only capable of handling thecomplex nonlinear morphological phenomena we are about to describe but also theusual linear ones found in many languages The framework is a multitiered modelthat encompasses linear and nonlinear morphology

The elegance of the proposed framework lies in the fact that it is capable of han-dling sophisticated linguistic descriptions such as those of autosegmental phonologyin a computationally tractable way The model consists of three components The rstis a multitier lexicon that consists of several sublexica each describing a lexical tieras in autosegmental phonology The second component is a bidirectional rewrite rulessystem that maps inter alia the multitier lexical representations to a linearized surfaceform and vice versa The third component provides morphotactic constraints The pro-posed framework has the computational property that its lexical and rule formalismsare compiled algorithmically into nite-state machinery using operators under whichnite-state machines are closed

700 Mountain Ave Murray Hill NJ 07974 E-mail gkirazresearchbell-labscom

c 2000 Association for Computational Linguistics

Computational Linguistics Volume 26 Number 1

The rest of this section discusses the importance of nonlinear morphology andoutlines the research objectives of this work

11 Nonlinear MorphologyEarly generative morphophonological theory was mainly based on the linear segmen-tal approach of The Sound Pattern of English (Chomsky and Halle 1968) In the midseventies however linguists had departed from this linear framework to a nonlinearone Goldsmith (1976) working on the phonology of African tone languages pro-posed autosegmental phonology with multitiered representations Goldsmith madeuse of two tiers to describe tone languages one to represent sequences of vowelsand consonants and another to describe tone segments McCarthy (1979) applied au-tosegmental phonology to Semitic root-and-pattern morphology resulting in what isnow known as the theory of nonconcatenative (or nonlinear) morphology as opposedto concatenative morphology McCarthyrsquos ndings have become ubiquitous In factldquoevery aspect of the theory of morphology and morphophonologyrdquo remarks Spencer(1991 134) ldquohas had to be reappraised in one way or another in the wake of [Mc-Carthyrsquos] analysis of Semitic and other languagesrdquo

Spencerrsquos statement could well apply to the theory of computational morphologyTwo-level morphology (Koskenniemi 1983) as well as its predecessor in the work ofKay and Kaplan (1983) is also deeply rooted in the linear concatenative tradition In-deed ldquoif Koskenniemi had been interested in Arabic or Warlpiri rather than Finnishrdquonotes Sproat (1992 206) ldquohis system might have taken on a rather different characterfrom the startrdquo It would prove difcult if not impossible to implement Semitic lan-guages using linguistically motivated theoretical models such as those of McCarthyand others in the eld with traditional two-level morphology

Kay (1987) was the rst computational linguist to make use of McCarthyrsquos nd-ings He proposed that a four-tape nite-state machine as opposed to the traditionaltwo-tape machines of two-level morphology be used to describe the autonomousmorphemes of Arabic Kay devised a system for manipulating the multitape machinealbeit using an ad hoc procedure to control the movements of the machinersquos head(s)We shall build upon Kayrsquos work by providing higher-level lexical and rule formalismsand algorithms for compiling the formalisms into multitape machines eliminating theneed for the ad hoc procedure that controls head movements We shall revisit Kayrsquosapproach in Section 61

Previous work to implement Semitic languages namely Akkadian (Kataja andKoskenniemi 1988) Arabic (Beesley Buckwalter and Newton 1989 Beesley 1990 19911996 1998a 1998b 1998c forthcoming) and Hebrew (Lavie Itai and Ornan 1990)employed traditional two-level morphology with some augmentation to handle thenonlinearity of stems but did not make any use of the then-available theory of non-concatenative morphology The challenge here lies in the fact that two-level morphol-ogy assumes the lexical representation of a surface form to be the concatenation ofthe corresponding lexical morphemes in question To resolve the problem these au-thors (with the exception of Beesleyrsquos work from 1996 on) provided for a simultaneoussearch of various root and afx lexica the result of which served as the lexical tape ofthe two-level system We shall revisit these approaches in Sections 62 and 63

Other publications dealing with Semitic computational morphology are connedto proposals for compiling autosegmental descriptions into automata (Kornai 1991Wiebe 1992 Bird and Ellison 1992) They revolve around encoding autosegmentalrepresentations (by various encoding mechanisms) and providing ways for compilingsuch encodings into nite machines None provide for lexicon and rule formalismsthat can be compiled into their respective encodings or directly into automata No

78

Kiraz Multitiered Nonlinear Morphology

Semitic language to the best of the authorrsquos knowledge has been implemented withthese proposals We shall revisit these approaches in Section 64

12 Research ObjectivesThe purpose of this work is to provide a theoretical computational framework underwhich nonlinear morphology can be handled in a linguistically and computationallymotivated manner with the following objectives in mind

1 The framework is to present a general multitiered computationalmorphology model that allows for both linear and nonlinearmorphophonological descriptions

2 The formalism of the framework is to handle various linguistic theoriesand models including McCarthyrsquos initial ndings as well as later modelsfor Hebrew (Bat-El 1989) moraic theory (McCarthy and Prince 1990a1995) the afxational approach to handling templates in Arabic(McCarthy 1993) and others That is a exible formalism that leaves thegrammar writer with ample room to choose the appropriate linguistictheory for an application

3 Multitiered lexica and grammars written in the formalism are to becompiled into nite-state machines (multitape automata in this case) Themultitape machines are created by a compiler that employs a nite-stateengine with an algebraic interface to n-way regular expressions

4 The multitape machines are to be as close as possible in spirit totwo-level morphology in that surface forms map to lexical morphemesOur lexical level is a multitiered representation

This paper provides an overall description of the theoretical framework compila-tion algorithms and illustrations Additionally it discusses other related topics crucialto developing Semitic grammars

Results that emerged earlier from this work appear elsewhere (Kiraz 1994b 19961997a 1997b 1997c in press) but have been thoroughly enhanced and reworked sinceNew contributions include enhancing the theoretical framework (Section 3) compilinglexica and rules into multitape nite-state machines (Section 4) and evaluating thecurrent model with respect to previous ones (Section 6)

2 Problems in Semitic Morphophonology

The challenges in implementing Semitic morphophonological grammars are numer-ous Here we shall concentrate only on nonlinearity that poses computational dif-culties to traditional nite-state models

21 The Nonlinear StemThe main characteristic of Semitic derivational morphology is that of the ldquoroot and pat-ternrdquo The ldquorootrdquo represents a morphemic abstraction usually consisting of consonantseg ktb lsquonotion of writingrsquo Stems are derived from the root by the superimpositionof patterns A ldquopatternrdquo (or ldquotemplaterdquo) is a sequence of segments containing Cs thatrepresent the root consonants eg C1aC2C2aC3 and maC1C2aC3 (the indices refer toroot consonants) Root consonants are slotted in in place of the Cs to derive stemseg Arabic kattab lsquowrotersquo and maktab lsquoofcersquo from the root ktb and the abovetwo patterns respectively

79


Table 1Syriac verbal stems with the root ktb The dataprovides stems in underlying morphological formssurface forms are parenthesized The passive ismarked by the reexive prex et

Measure Active Passive ( et +)

P al (1) katab (ktab) kateb ( etkteb)Pa el (2) katteb kattabaf el (3) akateb ( akteb) akatab ( ettaktab)

Figure 1Autosegmental representations of Syriac Measures 1-3 Each morpheme sits on its ownautonomous tier

22 Various Linguistic ModelsThere are various linguistic models for representing patterns In traditional accountsthe ldquovocalismrdquo (ie vocalic elements) is collapsed with the pattern (Harris 1941)eg maC1C2aC3 above Since the late 1970s however more sophisticated descriptionshave emerged most notably by McCarthy (1981 1986 1993) and McCarthy and Prince(1990a 1990b 1995)

Consider the Syriac verbal data in Table 1 containing verbs classied according tovarious measures1 Glancing over the table horizontally one notes the same patternof consonants and vowels per measure the only difference is that the vowels areinvariably ae in active stems but aa in passive stems (apart from Measure 1whose vocalism is idiosyncratic a general Semitic phenomenon) Surface forms thatresult after phonological rules are applied appear in parentheses The vowel after [k]in the Measure 1 and 3 forms for example is deleted because it is a short vowel in anopen syllable a general phenomenon of Aramaic (of which Syriac is a dialect) Further[ ] in the passive of Measure 3 is assimilated into the preceding [t] of the reexiveprex Both rules are employed in et akatab ettaktab

Under McCarthyrsquos autosegmental analysis a stem is represented by three au-tonomous morphemes a consonantal root a vocalism and a pattern that consists ofCs and Vs For example the analysis of katteb (Measure 2) produces three mor-phemes the root ktb lsquonotion of writingrsquo the vocalism ae lsquo rsquo and thepattern CVCCVC lsquoMeasure 2rsquo Some stems include afx morphemes eg the prex

a of Measure 3 these sit on their own tier The segments are linked together by as-sociation lines as in Figure 1 Note the spreading of [a] in katab and the geminationof [t] in katteb

1 The term ldquomeasurerdquo is employed by native grammarians to denote a specic pattern

80


Figure 2Moraic analysis of the Arabic nominals Glosses appear under each autosegmental structureConsonants and vowels although shown on the same line belong to different tiers

While McCarthyrsquos initial model is the most visible in the computational linguisticsliterature it is by no means the only one McCarthy and Prince (1990b) argue forrepresenting the pattern morpheme in terms of the authentic units of prosody Considerthe Arabic nominal stems and their moraic analysis in Figure 2 Here a pattern isrepresented by a sequence of syllables s Association takes the following form asyllable node takes a consonant and its mora takes a vowel In bimoraic syllablesthe second may be associated with either a consonant or a vowel At the right edgeall stems end in an extrametrical consonant denoted by x

Other linguistic models have been described by Hammond (1988) Bat-El (1989)and McCarthy (1993)

23 Orthographic IssuesIn addition to the linguistic peculiarities of Semitic the writing system adds furthercomplications The vast majority of Semitic texts (apart from Ethiopic) are orthograph-ically underspecied Short vowels are absent from the orthography (Imagine the pre-vious sentence had been written ldquoshrt vwls r bsnt frm th rthgrphrdquo) We shall dealwith vocalization issues in Section 54

3 The Theoretical Framework A Multitiered Model

The model presented here assumes two levels of linguistic description in recognitionand synthesis The lexical level employs multiple representations (eg for patternsroots and vocalisms) while the surface level employs only one representation Theupper bound on the number of lexical representations is not only language-specicbut also grammar-specic

The proposed model is divided into three components (i) a lexicon componentwhich consists of multiple sublexica each representing entries for a particular lexicalrepresentation or tier (ii) a rewrite rules component which maps the multiple lexicalrepresentations to a surface representation and (iii) a morphotactic component whichenforces morphotactic constraints

Throughout the following discussion a tuple of strings represents a surface-to-lexical mapping where the rst element of the tuple represents the surface form andthe remaining elements represent lexical forms For instance the tuple of strings thatrepresents the mapping of katab to its lexical forms is katabcvcvcktba 2 Theelements are surface pattern root vocalism

2 Capital-initial strings will be used shortly to denote variables For this reason we represent the patternusing small letters

81


31 The Lexicon ComponentHere the lexicon consists of multiple sublexica each sublexicon containing entries forone particular lexical representation (or tier in the autosegmental analysis) Since an n-tuple contains n 1 lexical elements (the rst element is the surface representation) thelexicon component consists of n 1 sublexica A Syriac lexicon for the data in Table 1requires a pattern sublexicon a root sublexicon and a vocalism sublexicon Otherafxes that do not conform to the root-and-pattern nature of Semitic morphology (egthe reexive prex et ) can either be given their own sublexicon or placed in oneof the three sublexica Since pattern segments are the closestmdashin terms of numbermdashto surface segments such morphemes are represented in the pattern sublexicon byconvention

As a way of illustration the rst sublexicon for the Syriac data in Table 1 containsthe following entries et (representing the reexive prex) and cvcvc (for theverbal pattern) Here we have chosen to derive all verbs from this pattern in a wayreminiscent of McCarthy (1993) rather than entering separate patterns for each mor-pheme The second sublexicon maintains roots eg ktb lsquonotion of writingrsquo pnqlsquonotion of delightrsquo and qrb lsquonotion of approachingrsquo The third sublexicon maintainsvocalisms ae for active stems and a (with spreading) for passive ones

32 The Rewrite Rules ComponentThe rewrite rules component maps the multiple lexical representations to a surfacerepresentation and vice versa It also provides for phonological orthographic andother rules The current model adopts the formalism presented by Ruessink (1989)and Pulman and Hepple (1993) with additional extensions to handle multiple lexicalforms Below the top line represents the lexical tiers and the bottom line representsthe corresponding surface form

LLC RLC LSC RSC

denotes the left lexical context denotes the lexical form and denotesthe right lexical context and are the surface counterparts The con-text denoted by ldquordquo represents Kleene star as applied to the grammar alphabet (iematching anything) When all four contexts are ldquordquo they are omitted from rules iethe formalism becomes

Further capital-initial expressions are variables over predened nite sets of symbolsThe operator is the optional operator It states that may surface as

in the given context but may surface otherwise if sanctioned by another rule Theoperator adds obligatory constraints when appears in the given context thenthe surface description must satisfy A lexical string maps to a surface string ifand only if they can be partitioned into pairs of lexical-surface subsequences where (i)each pair is licensed by a rule and (ii) no sequence of zero or more adjacent pairsviolates a rule The interpretation of the latter condition is based on Grimley-EvansKiraz and Pulman (1996) (See Kiraz [in press] for the historical development of theformalism)

Several extensions are introduced into the formalism to handle multitiered repre-sentations Expressions on the upper lexical side ( and ) are tuples ofstrings of the form x1 x2 xn 1 The ith element in the tuple refers to symbols inthe ith sublexicon of the lexical component When a lexical expression makes use of

82


cXR1 X

where X is a consonantv X

R2 Xwhere X is a vowel

v X cv R3

where X is a vowel

Figure 3Rules for the derivation of Syriac ktab R1 and R2 sanction root consonants and vowelsrespectively while R3 handles vowel deletion

Figure 4Lexical-surface analysis of Syriac ktab and etktab Vocalic spreading is ignored in thisexample (see Section 51)

only the rst sublexicon the angle brackets can be ignored Hence the expressionx and x are equivalent in lexical contexts x and x are equivalent

Additionally the symbol ldquordquo now denotes Kleene star as applied to the alphabet ofthe respective tier

The formalism is illustrated in Figure 3 The rules derive Syriac ktab (underlyingkatab) from the pattern morpheme cvcvc lsquoverbal Measure 1rsquo the root morphemektb lsquonotion of writingrsquo and the vocalism morpheme aa lsquo rsquo (ignoring

spreading for the moment) Rule R1 sanctions root consonants by mapping a [c] fromthe rst (pattern) sublexicon a consonant [X] from the second (root) sublexicon and nosymbol from the third (vocalism) sublexicon to surface [X] Rule R2 sanctions vowelsin a similar manner The obligatory rule R3 deletes the rst vowel of katab in thegiven context The mapping is illustrated in Figure 4(a) The numbers between thesurface and lexical expressions indicate the rules in Figure 3 that sanction the shownsubsequences Empty slots represent the empty string

As stated above morphemes that do not conform to the root-and-pattern nature ofSemitic (eg prexes sufxes particles) are given in the rst sublexicon The identityrule

XR0 X

where X c v

maps such morphemes to the surface The rule basically states that any symbol not

83


Table 2Syriac circumxes of theimperfect verb

Number Gender Circumx

Sing masc ne-Sing fem te-Pl masc ne-unPl fem te- Ecircan

in cv from the rst sublexicon may optionally surface Figure 4(b) illustrates theanalysis of etkatab from the morphemes given earlier

33 The Morphotactics ComponentSemitic morphotactics is divided into two categories Templatic morphotactics occurswhen the pattern root vocalism and possibly other morphemes join together in anonlinear manner to form a stem Non-templatic morphotactics takes place when thestem is combined with other morphemes to form larger morphological or syntacticunits The latter is divided in turn into two types linear nontemplatic morphotacticswhich makes use of simple prexation and sufxation and nonlinear nontemplaticmorphotactics which makes use of circumxation

Templatic morphotactics is handled implicitly by the rewrite rules component Forexample the rules in Figure 3 implicitly dictate the manner in which pattern root andvocalism morphemes combine Hence the morphotactic component need not worryabout templatic morphotactics

Linear nontemplatic morphotactics is handled via regular operations usually n-way concatenation (Kaplan and Kay 1994) in the multitiered case Consider for ex-ample Syriac etktab and its lexical analysis in Figure 4(b) The lexical analysis ofthe prex is et and that of the stem is cvcvc ktb aa Their n-way concatena-tion gives the tuple et cvcvc ktb aa One may also use the ldquocontinuation classesrdquoparadigm familiar from traditional two-level systems (Koskenniemi 1983 inter alia)in which lexical elements on each sublexicon are marked with the set of morphemeclasses that can follow on the same sublexicon

The last case is that of nonlinear nontemplatic morphotactics Normally this arisesin circumxation operations The following morphotactic rule formalism is used todescribe such operations

A P B S

P S p1 s1

P S p2 s2

P S pn sn

A circumx here is a pair P S where P represents the prex portion of the circumx

and S represents the sufx portion The circumxation operation PBS applies thecircumx P S to B By way of illustration consider the Syriac circumxes of theimperfect verb in Table 2 The circumxation of the circumxes to the stem Syriac

84


ktob lsquoto write ndash rsquo is

Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan

Unlike traditional nite-state methods in morphology that employ two-tape trans-ducers the proposed multitiered model requires multitape transducers The algorithmsfor compiling the three components into such machines are given next

4 Algorithms for Compilation into Multitape Automata

Multitape nite-state machines were rst introduced by Rabin and Scott (1959) and El-got and Mezei (1965) An n-tape nite-state automaton (FSA) is a 5-tuple Q q0 F where Q is a nite set of states is a nite input alphabet Q n 2Q is atransition function (where and is the empty string) q0 Q is aninitial state and F Q is a set of nal states An n-tape FSA accepts an n-tuple ofstrings if and only if starting from the initial state q0 it can simultaneously scan allthe symbols on every tape i 1 i n and end up in a nal state q F An n-tape nite-state transducer (FST) is simply an n-tape nite-state automaton but witheach tape marked as to whether it belongs to the domain or range of the transduc-tion

In addition to common operators under which nite machines are closed thealgorithms discussed below make use of the following three operators

DenitionLet L be a regular language n L X X is an n-tuple of the form x x x

L is the n-way identity of L

DenitionLet R be a regular relation over the alphabet and let m be a set of symbols not neces-

sarily in m R inserts the relation n a for all a m freely throughout R

The identity and insert operators are the n-tape version of their counterparts inKaplan and Kay (1994)3

DenitionLet S and S be same-length n-tuples of strings over some alphabet I n a

for some a and S S1IS2I Sk k 1 such that Si does not contain I ieSi

n I We say that S I S S1S S2S Sk substitutes everyoccurrence of I in S with S

3 Insert is also called the ignore operator eg in the Xerox nite-state compiler (Karttunen and Beesley1992 Karttunen 1993)

85


Figure 5Multitape representation of the lexicon

41 Building a Multitape LexiconThe compilation process builds a one-tape automaton for each sublexicon The sub-lexica are then put together using the cross product operator with the effect that theresulting machine accepts entries from the ith sublexicon on its ith tape

Representing a lexical entry W in an automaton is achieved by concatenating thesymbols of W one after the other Now let i W1 W2 be the set of lexicalentries in the ith sublexicon The expression for the ith sublexicon becomes

LiW i

W 1

(Daciuk et al [2000] give a more sophisticated incremental algorithm for compilingacyclic lexica)

The overall lexicon can then be expressed by taking the cross product of all thesublexica To make the nal lexicon accept same-length tuples we insert 0s throughout

Lexiconn 1

i 1

Li 2

All invalid tuples resulting from the cross product operation (eg 00 0 ) areremoved by the intersection with where is the set of all feasible tuples computedfrom rules (see Section 42) By way of illustration Figure 5 gives the lexicon for thepattern cvcvc the roots ktb pnq qrb and prq and the vocalism ae

42 Compiling the Rewrite Rules ComponentThe algorithm for compiling rewrite rules is based on collaborative work by the authorwith E Grimley-Evans and S Pulman (Grimley-Evans Kiraz and Pulman 1996) Thecompilation process is preceded by a preprocessing stage during which all mappingsof unequal lengths are made same-length mappings by inserting a special symbol 0when necessary (The grammar writer need not worry about this special symbol butcannot use it in the grammar) This is necessary because -containing transducers arenot closed under intersection and subtraction Additionally during preprocessing thefollowing sets are computed the set of all feasible tuples sanctioned by the grammar

(used in expression (2) above) and the set of feasible surface symbols s (to be usedin expression (23) in Appendix A)

The actual compiler takes as its input rules that have been preprocessed Thealgorithm is subtractive in nature it starts off by creating an automaton that acceptssequences of feasible tuples that are sanctioned by rules regardless of context thenstarts subtracting strings which violate the rules This subtractive approach was rstsuggested by E Grimley-Evans

86


Figure 6A four-tape machine for accepting centers The symbol s denotes the partition symbol Thesurface symbol appears to the left of ldquordquo and the lexical tuple to its right

421 Accepting Centers Recall that in the formalism of Section 32 a lexical stringmaps to a surface string if and only if they can be partitioned into pairs of lexical-surface subsequences where (i) each pair is licensed by a rule and (ii) no sequenceof zero or more adjacent pairs violates a rule

Let c s l1 l2 be the center of a rule where s is the surface form and li are thelexical forms and let C be the set of all such centers in the grammar Further let bea special symbol (not in the grammarrsquos alphabet) to denote a subsequence boundarywithin a partition and let n The automaton that accepts the centers of thegrammar is described by the relation

Centers C 3

Centers accepts any sequence of the centers described by the grammar (each cen-ter surrounded by ) irrespective of their contexts Assuming that ktab is underconsideration Figure 6 gives the four-tape machine for the centers of the rules fromFigure 3

422 Valid Contexts Now we eliminate all the sequences whose left and right con-texts violate the grammar For each center c C in the entire grammar let LRc

1 1 2 2 be the set of valid left and right context pairs for that center Theinvalid contexts for c are expressed by

Restrict c LRc

c 4

The rst component of expression (4) gives all the possible contexts for c The sec-ond component gives all the valid contexts for c The subtraction results in all theinvalid contexts for c However since appears freely in expression (3) it needs to beintroduced in expression (4) as well resulting in

Restrict c LRc

c 5

The relation in expression (5) works only if the center consists of just one tuple Inorder to allow it to be a sequence of tuples c must be surrounded by on both sides

87


Figure 7The machine from Figure 6 is repeated here after processing the rules in Figure 3

to mark it as one subsequence It also must be devoid of any The rst conditionis accomplished by simply placing to the left and right of c As for the secondcondition an auxiliary symbol is used as a placeholder representing c in order toavoid inserting within the tuples of c by Hence rst we introduce freelyusing then substitute c back in place of

Restrict (6)

c

LRc

where n Finally for each c we subtract all such invalid relations fromCenters yielding the relation

ValidContexts Centersc

Restrict 7

ValidContexts now accepts all the sequences of tuples described by the grammar basedon their contexts however it does not enforce obligatory rules Figure 7 gives themachine after the center of R3 from Figure 3 has been processed

423 Obligatory Rules For each obligatory rule let represent the center c with thecorrect lexical expressions and the incorrect surface expression The following relationdescribes all sequences of tuples that contain an unlicensed segment

Coerce LR

8

The two s surrounding ensure that obligatoriness applies to at least one lexical-surface subsequence The operator inserts additional s through the contextsand the center The insertion of through the center allows Coerce to apply to a seriesof lexical-surface subsequences To handle the case of epenthetic rules one needs toallow Coerce to apply on zero subsequences as well In such a case one takes the unionof expression (8) with ie the empty subsequence

Finally we subtract Coerce from the ValidContexts relation yielding the relation

Rules ValidContexts Coerce 9

88


Figure 8The machine from Figure 7 is repeated here after processing the obligatory rule R3 fromFigure 3

The relation accepts all and only the sequences of tuples described by the grammarFigure 8 gives the machine after processing the obligatoriness of rule R3 The last stepin compiling rules is to remove all instances of the symbol and the symbol 0

43 Compiling the Morphotactic ComponentThe only class of morphotactics that is of interest here is nonlinear nontemplatic cir-cumxation per the formalism in Section 33 Let P S p1 s1 p2 s2 pn snbe a set of circumxes and let B be the domain of the circumxation operation A rule

A PBS is compiled into an automaton by the expression in (10)

Aps PS

pBs 10

An equivalent approach to handling circumxation is to follow the subtractive ap-proach used in compiling the rewrite rules component above by rst overgeneratingand then subtracting all invalid forms The two approaches union or subtraction areformally equivalent in that they result in the same machine Compilation using theunion approach however is more efcient in terms of time complexity than the sub-tractive approach The latter requires invoking negation and intersection algorithmsboth of which are computationally expensive It must be noted that the union approachrequires a great deal of care in creating a machine that accepts only grammatical formswith no overgeneration

Beesley (1998c) employed a similar approach for eliminating invalid forms in Ara-bic long-distance dependencies by means of composition

5 Developing Semitic Grammars

When developing Semitic grammars various issues and problems arise that normallydo not occur with linear grammars This section aims at pointing out some of theseissues

51 Handling the Nonlinear StemThe example lexica and rules in Sections 31 and 32 demonstrate how the CV-basedtemplates are implemented in the current framework Further spreading and gemina-tion which tend to cause difculties in other computational frameworks (see Section 6)are represented easily in the multitiered model without having to resort to ad hoc no-tation For example the following rule which uses prosodic templates demonstrates

89


the intrasyllabic spreading of vowels

Intrasyllabic spreading C V

CVV

Extrametricality x CC

The symbol above is a templatic segment denoting a bimoraic syllable The rulestates that when appears on the pattern tape a consonant C and a vowel V are readfrom the root and vocalism tapes respectively the corresponding surface segments areCVV In conjunction with the extrametricality rule above one obtains surface-lexicaltuples like ˆaamuus x ˆms au where the element to the left of ldquordquo is thesurface form and the tuple to its right represents the lexical forms (see Figure 2(d))

Gemination is handled in one of two ways The rst marks pattern consonantalsegments (C or s) with a subscript (eg c1vc2vc3) and provides rules to geminate theappropriate consonant eg

Gemination in kattab c2 XXX

The second approach leaves pattern segments unmarked but provides the properleft and right contexts in rules The former approach requires more annotations inlexica and rules but provides for smaller machines since no context expressions areused The opposite holds for the later approach Both however require rule features(see Section 52) to ensure that the rule applies only to the desired measures

As the multitiered framework does not put any limitations on the number of lexicaltapes the grammar writer may also choose to place afxes on their own autonomoustape Hence one produces surface-lexical tuples like akateb a cvcvc ktb ae (seeFigure 1(c))

52 Using Features to Handle IdiosyncraciesVarious lexical and morphotactic constraints exist in Semitic For instance roots donot appear in all verbal measures rather each root occurs in the literature in a subsetof the measures eg pnq does not exist in Measure 1 (one gets such informationfrom dictionaries and corpora) Another example is that the vocalisms of Measure1 in almost all Semitic languages are lexically marked for each root In the currentframework categories of the form

1 1

2 2

are used in the lexicon as well as rules to resolve such issues (Bear 1988 Ritchie et al1992) Here a value can be either an atom or a set of atoms For example the set ofmeasures in which a root occurs are given in the attribute below

ktba

pnq

qrbe

90


The vocalisms of Measure 1 for various roots are marked with the attribute Hence one gets [a] in ktab but [e] in qreb

Categories are also used in rules For example the gemination rule above is asso-ciated with a category that indicates the measures in which gemination is valid Thedenition of rule obligatoriness is extended to include categories (Pulman and Hepple1993) The categories are incorporated in the automata compilation process followingthe algorithms in Kiraz (1997a)

53 Linear versus Nonlinear GrammarsConsidering that nonlinearity in Semitic occurs mainly in the stem maintaining anonlinear lexical representation in rewrite rules causes rules that describe one phono-logicalorthographic phenomenon to be duplicated This becomes a challenge to thegrammar writer since Semitic employs very rich phonological rules assimilation dis-similation prosthesis anaptyxis syncope haplology etc (Moscati et al 1969 Sec-tion 91 ff)

Consider the derivation of Syriac ktab using the rules in Figure 3 Since voweldeletion in Syriac applies right-to-left when adding the object pronominal sufx ehlsquo rsquo the second vowel should be deleted katabeh katbeh Byvirtue of its right lexical context however R3 in Figure 3 can only apply to the rststem vowel Another rule (R4 below) is required for deriving katbeh from kataband the sufx eh where the second stem vowel is deleted

v cV R4

where V is a vowel

The c in the right lexical context is a concrete symbol from a pattern morpheme whileV represents the class of all vowels

This does not resolve the problem Both R3 and R4 fail when the deleted vowelitself appears in the prex eg wakatbeh wkatbeh (with the prex wa )requiring another rule An additional rule is also needed to delete prex vowels whenthe right context belongs to a (possibly another) linear prex eg prexing the se-quence wa lsquoandrsquo la lsquotorsquo and da lsquoofrsquo to the stem katab giving waldaktab(the [a] of la and the rst stem vowel are deleted)

The above examples clearly illustrate the proliferation that would result Consid-ering that such phonological rules do not depend on the nonlinear lexical structureof the stem a better approach divides the lexical-surface mappings into two separateproblems The rst handles the templatic nature of morphology mapping the multi-ple lexical representation into a linearized lexical form somewhat corresponding toMcCarthyrsquos notion of tier conation (McCarthy 1986) Linearization of autosegmentalrepresentations in general has been suggested earlier by Kornai (1991 1995)

The second takes care of phonologicalorthographicgraphemic mappings be-tween the linearized lexical form and the actual surface The entire grammar is takenas the composition of two sets of rules (Karttunen Kaplan and Zaenen 1992) Com-position however needs to be dened for multitape machines First we redene ann-tape nite-state machine as Q q0 F d where the rst ve elements are as be-fore and d 1 d n is the number of domain tapes (the number of range tapes issimply n d)

DenitionLet A Q1 1 1 q1 F1 d1 and B Q2 2 2 q2 F2 d2 be two multitape machines

over n1 and n2 tapes respectively Further let si denote the symbol on the ith tape

91


There is a composition of A and B denoted by C if and only if d2 n1 d1 withC Q1 Q2 1 2 q1 q2 F1 F2 d1 where for all p1 Q1 and p2 Q2

p1 p2 s1 sd1 sd2 1 sn2

1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2

if and only if sd1 1 s1 sn1 sd2

The resulting machine is an k-tape machine where k d1 d2 n2 In our imple-mentation (see Section 7 and Appendix A) the domain and range tapes are given asarguments to the composition function rather than coding them in machines in orderto allow for exibility in using machines

54 VocalizationSemitic texts appear in three forms consonantal texts which do not incorporate anyvowels but matres lectionis partially vocalized texts which incorporate some vowelsto clarify ambiguity and vocalized texts which incorporate full vocalization

Handling all such forms is resolved in line with the previous discussion on lin-earization The grammar writer should assume full vocalization when writing gram-mars This will not only get rid of the duplicated rules for the same phonologi-calorthographic phenomenon but will also make understanding and debugging rulesan easier task Once a lexical-surface rewrite rules system has been achieved a set ofrules that optionally delete vowel segments are specied and composed with the entiresystem

6 Other Approaches to Finite-State Semitic Morphology

61 Kayrsquos Multitape ApproachKay (1987) proposed handling the autosegmental analysis of Arabic by means of mul-titape automata Kay adds some extensions to traditional FSTs Transitions are markedwith quadruples of elements (for vocalism root pattern and surface form respec-tively) where each element is a pair a symbol and an instruction concerning themovement of the tapersquos head Kay uses the following notation An unadorned symbolis read and the tapersquos head moves to the next position A symbol in brackets [ ] isread and the tapersquos head remains stationary A symbol in braces is read and thetapersquos head moves only if the symbol is the last one on the tape

The transitions for the analysis of Syriac kattab lsquoto writemdash rsquoexcluding the reexive prex et are shown in Figure 9 After the rst transitionon the quadruple [ ] k C k in Figure 9(a) no symbol is read from the vocalismtape [k] is read from the root tape and the tapersquos head is moved [C] is read from thepattern tape and the tapersquos head is moved and [k] is written on the surface tape andthe tapersquos head is moved At the nal conguration all the tapes have been exhaustedKay makes use of a special symbol G to handle gemination when read a symbolfrom the root tape is scanned without advancing the read head of that tape

The model suffers from a number of shortcomings some of which have alreadybeen pointed out (Bird and Ellison 1992 Section 51) Firstly the use of various bracket-ing notations to control the moves of the machine head(s) causes the read heads of thethree upper input tapes to move independently of each other this put the expressive-ness of the device under question Bird and Ellison (1992 but not 1994) questioned theformal power of the device Wiebe (1992) citing formal results from Fischer (1965)

92


Figure 9Kayrsquos Analysis of Syriac kattab The four tapes are (from top to bottom) vocalism tape roottape pattern tape and surface tape Transition quadruples are shown at the right side of thetapes The symbol ldquo rdquo between the lower surface tape and the lexical tapes indicates thecurrent symbols under the readwrite heads

stated that Kayrsquos machine goes beyond nite-state power No consensus has beenreached on the matter to the best of the authorrsquos knowledge In contrast our pro-posed n-tape machines move all the read heads simultaneously ensuring nite-stateexpressive power Secondly the introduction of ad hoc symbols to templates (eg Gfor gemination) moves away from the spirit of association in autosegmental phonologythat Kay wanted to model other special symbols must also be added to completelyimplement the rest of the paradigm in question

We have demonstrated however the usefulness of Kayrsquos proposal Indeed if oneeliminates the ad hoc controls of the read head(s) and provides a rule formalismfrom which machines can be compiled algorithmically the multitape model is quiteadequate for describing autosegmental representations

62 The Intersection of Lexica ApproachKataja and Koskenniemi (1988) working on Akkadian developed a system undertraditional two-level morphology It was mentioned earlier (see Section 11) that thechallenge of handling Semitic morphology within traditional two-level morphology isthat the lexical level is not merely the concatenation of the morphemes in question

Kataja and Koskenniemi resolved this by devising a ldquolexicon componentrdquo thatmakes use of two lexica one for roots and the other for stem patterns and afxesEntries in the former leave afx elements unspecied while entries in the latter leaveroot elements unspecied For example the lexical entry for the Arabic root morphemektb takes the form

p k p t p b p 11

where p is the alphabet of nonroot segments likewise the entry for the perfect passivevocalism ui takes the form

r u r i r 12

where r is the alphabet of root segments The intersection of both expressions allowsfor the well-formed string kutib as well as numerous ill-formed sequences such asktbui inter alia Under this framework the result of the intersection becomes the

93


lexical level of a traditional two-level morphology system The two-level system thentakes care of other morphological phonological and orthographic rules all of whichare linear in nature Kataja and Koskenniemi suggested simulating the intersection byhaving the lexical lookup explore both lexica simultaneously

The following computational shortcomings of the intersection approach come tomind The intersection of the two lexica works only if p and r are disjoint As thisis not the case in Semitic one has to introduce ad hoc symbols in the alphabet tomake the two alphabets disjoint Alternatively Beesley (forthcoming) introduces aningenious but cumbersome bracketing mechanism Expression (11) above becomes

A k A t A b A 13

where A (I have changed Beesleyrsquos curly brackets into angle brackets inorder to avoid confusion with set notation) Expression (12) then becomes

B u B i B 14

where B V and V is the disjunction of all vowels Finally each measure is givenby an expression for instance Arabic Form V (eg takattab where the rst [t] is anafx not related to the [t] of the root) is

tVCVCXVC 15

where C isktb 16

(ie the disjunction of the root symbols surrounded by angle brackets) The symbolX in expression (15) indicates gemination in a way reminiscent of Kayrsquos G symbolThe intersection of expressions (13) (14) and (15) results in takatXab (X is dealtwith by later rules) The disjunction of all such intersections results in what one maycall a ldquoquasi lexiconrdquo ie the lexical side of subsequent two-level transducers thatdeal with linear phenomena (setting aside long-distance dependencies) Given r roots(approximately 4000 in Modern Standard Arabic) v vocalisms and p patterns (a fewhundred for v p depending on the linguistic framework used) Beesleyrsquos bracketingalgorithm needs to perform m intersections where r m r v p (since each rootonly intersects with lexically dened subsets of the patterns) In contrast such a brack-eting mechanism is not necessary in our multitape approach since the alphabet of onetape does not interfere with the alphabets of other tapes Further our lexicon compilerneeds to perform only n 1 cross product operations (where n is the number of lex-ical tapes usually 3) There is a substantial time complexity difference with practicaleffects A faithful implementation of Beesleyrsquos bracketing approach and ours was per-formed using the Bell Labs Lextools compiler (Sproat 1995 Kiraz 1997b) (See Sproat[1997 Section 32] for a brief description of Lextools) The test was also performed byM Jansche using a neutral nite-state library (van Noord 1997) to ensure partialityJansche was able to substantially enhance the performance of Beesleyrsquos method Theresults of compiling various numbers of roots with the 24 Arabic verbal patterns ap-pear in Table 3 The table indicates that for a full-scale system the proposed multitiercompilation method is far more efcient Details of the tests appear in Appendix B

More serious is the fact that bidirectionality of two-level morphology (ie mor-phemes mapping to surface forms and vice versa) is lost Once intersection is per-formed the result is an accepting automaton that represents stems rather than inde-pendent morphemes In contrast using our multitape model the original morphemes

94


Table 3Evaluation of lexical compilation of Beesleyrsquos bracketing mechanism vsKirazrsquos multitiered method using Lextools and van Noordrsquos FSA utilitiesThe times of the compilation process for the latter are based on anenhanced implementation of Beesleyrsquos method by M Jansche (seeAppendix B) The ratio columns show the order of complexity (eg for100 roots the multitiered lexical compilation runs 237 times faster thanBeesleyrsquos bracketing mechanism using Lextools and 49 times faster thanJanschersquos enhancements to Beesleyrsquos algorithm)

Lextools Van Noordrsquos

Roots Beesley Kiraz Ratio Beesley-Jansche Kiraz Ratio(h min sec) (sec) (sec) (sec)

20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980

(root pattern and vocalism) can be reconstructed from the multitape lexicon by aprojection operation Hence projection under which automata are closed acts as theldquoreciprocalrdquo operator for cross product in expression (2) ensuring means for bidi-rectionality There is no such reciprocal operator for intersection it is a destructiveoperator in the sense that its arguments cannot be recovered from the result

63 Beesleyrsquos Other ldquoIntersectionrdquo ApproachBeesley and his colleagues (Beesley Buckwalter and Newton 1989 Beesley 1990 1991)developed a large-scale Arabic system under two-level morphology which even hasthe ability to handle regional Egyptian spelling (Beesley p c) The lexical lookup ofthe two-level model was augmented by a technique called ldquodetouringrdquo to access rootsand afxes from different lexica (see Sproat [1992 163ndash165] for details on ldquodetouringrdquo)In his 1996 paper and subsequent work Beesley reimplemented the system using theXerox lexical and rule compilers (Karttunen 1993 Karttunen and Beesley 1992) Anon-line demo of the reimplementation was also developed (Beesley 1998a)4

Bidirectionality is maintained in Beesleyrsquos system by a direct mapping of each rootand pattern pair to their respective surface realizations The lexical description givesthe root and pattern supercially concatenated in the form (Beesley 1996 p c)

[ktbampCaCaC] 17

The square brackets are special symbols that delimit the stem and ldquoamprdquo is another spe-cial symbol that separates the root from the pattern it is not the intersection operator

4 The new URL is httpwwwxrcexeroxcomresearchmlttarabic

95


For each root and pattern pair a rule of the following form is generated automatically

[ktbampCaCaC] katab 18

Each rule of the form in (18) is compiled into a transducer which is then appliedby composition to the identity transducer of the corresponding lexical description in(17) The result is a transducer that maps the string ldquo[ktbampCaCaC]rdquo into ldquokatabrdquo Itis worth noting that rules of the form in (18) are reminiscent of Chomskyrsquos earlytransformational rules for Hebrew stems (Chomsky 1951)

(As ldquoamprdquo in (17) and (18) is a concrete symbol no real intersection in the set-theoretic sense takes place though Beesley refers to this method as well as to thebracketing mechanism described in the previous section as ldquointersectionrdquo)

This method requires m (where r m r v p as before) rules of the formin (18) to be compiled into their respective transducers using algorithms of the Xeroxreplace operator (Karttunen 1997) literally thousands of rules Additionally the entireset of m transducers (or subsets one subset at a time) needs to be put together intoone (or more) transducer(s) by means of intersection (if the transducers are -free) orcomposition Although this takes place during developing the grammar rather thanat run-time the inefciency that results in the compilation process is apparent fromthe fact that a linguistic phenomenon (here the linearization of stems) is conveyed byapplying a rule to every single stem of the language As one does not provide a ruleto delete [e] in English move+ing and another to delete the same in charge+ingetc but a single [e] deletion rule that applies throughout the entire language stems inSemitic ought to be realized by rules that represent the phenomenon itself not everysingle instance of the phenomenon

In contrast the proposed multitier model requires only three rules throughout theentire language to model Beesleyrsquos roots and patterns (ie with X to denote geminationand hard-coding vocalic spreading) R1 (for stem consonants) and R2 (for stem vowels)from Figure 3 in addition to the following gemination rule (see Section 51 for ourhandling of gemination and spreading)

x C x Gemination C

where C is a consonant

The result of the three rules is a mere R 1 -state machine where R is the set of allroot segments (= 28 for Arabic 22 for Syriac) which is then applied to the multitieredlexicon Figure 10 gives such a machine for R= ktb and the vowels aui

Another disadvantage although a minor one of rules of the form in (18) is the lossof alignment between surface segments and their lexical counterparts While this doesnot affect the behavior of the resulting machines having segments aligned helps indebugging at the grammar-design stage A cursory look at the transitions in Figure 10indicates to the grammar writer the lexical segments that correspond to a surfacesegment

Having said that Beesleyrsquos system remains the largest reported Semitic grammarwritten within nite-state morphology to date The system however relies on oldlinguistic models as old as Harris (1941) No move has been reported to employ mod-ern linguistic models such as the autosegmental framework and other developmentsmentioned in Section 1 although this seems to be the direction of modern researchin computational Semitic morphology as well as linguistics (see the bibliographicalentries cited in Section 1)

96


Figure 10Rules for mapping multitier lexica into stems The symbol 0 represents

Figure 11Triangular prism demonstrating the autosegmental representation of Arabic kattab

64 Encoding Autosegmental Representations ApproachThere have been a number of proposals to encode autosegmental representationsKornai (1991 1995) gives a linear coding Wiebe (1992) and Bird and Ellison (1992)give a multitiered encoding We shall illustrate this approach from Bird and Ellisonrsquoswork

Every pair of autosegmental tiers constitutes a chart (or plane) The representationof Arabic kattab for example takes the form of a triangular prism as in Figure 11(Pulleyblank 1986) Each morpheme sits on one of the prismrsquos three longitudinal edgesthe pattern on edge 1-2 the vocalism on edge 3-4 and the root on edge 5-6 The prismhas three longitudinal charts pattern-vocalism (1-2-3-4) pattern-root (1-2-6-5) androot-vocalism (3-4-5-6) The corresponding encoding of the diagram is

Tier 1 a200Tier 2 C010 V100 C010 C010 V100 C010Tier 3 k010 t020 b010

Each expression is an n 1 -tuple where n is the number of charts The rst elementin the tuple represents the autosegment The positions of the remaining elements in thetuple indicate the chart in which an association line occurs and the numerals indicatethe number of association lines on that chart For example the expression a200 statesthat the autosegment ldquoardquo has two association lines on the rst pattern-vocalism chartzero lines on the second pattern-root chart and zero lines on the third root-vocalismchart

97


No implementation of a Semitic language to the best of the authorrsquos knowledgehas been carried out using these methods Bird and Ellison however give an exampleof how they envisage implementing Semitic using their framework For each mea-sure they provide an expression that generalizes over that particular measure eg forCVCCVC

C1 V0 C1 C1 V0 C1 19

The numbers after the colon refer to the autosegmental tier with which the segmentis linked (0 for vowels and 1 for root segments) A second expression generalizes overall stems constructed from a particular root eg for ktb

0 k1 0 t1 b1 20

where ldquordquo and ldquo+rdquo denote Kleene star and plus respectively A third expression de-scribes the vocalism eg for a with spreading

a C 21

The intersection of the three expressions per their intersection algorithm for suchencodings yields

k1 a0 t1 t1 a0 b1 22

Supercially this approach may seem equivalent to the other intersection ap-proaches mentioned in Section 62 The methodology here however is formally moreappealing and linguistically more sound since it provides for a mechanism to describeautosegmental association Bird and Ellison (1992 87) question if their approach willldquocover all possible generalizations about Arabic verbal structurerdquo It would denitelybe worth investigating how a higher-level autosegmental description of Semitic canbe compiled algorithmically into their machines directly

We mentioned above (Section 62) that the intersection approach lacks bidirec-tionality It is possible though this has not been tested that the indices in Bird andEllisonrsquos method can play a role in claiming the various morphemes of a particularsurface form

7 Implementation

There are two aspects of the implementation implementing the theoretical modelbased on the algorithms presented in Section 4 and implementing Semitic grammarsfor the case study As for the former the algorithms in Section 4 were implemented bythe author in SICStus Prolog Details of the implementation are given in Appendix A

As for the grammars themselves a small-scale Syriac grammar was implementedbased on the 100 most frequent roots including their numerous inexions of the Syr-iac New Testament (Kiraz 1994a) Care was taken however to ensure that most of theverbal and nominal classes of the language were exhaustively covered Additionallysample Arabic grammarsmdashbut with full coverage of the phenomena under questionmdashhave been implemented to test various linguistic models of Semitic including CVtemplates moraic templates afxational templatic morphology prosodic circumscrip-tion and broken plurals A detailed description of handling these linguistic modelsappears elsewhere (Kiraz in press)

8 Conclusion

This paper presented a multitier morphology model that can cope with the nonlinearoperations of Semitic root-and-pattern morphology in a linguistically motivated way

98


The system consists of three main components a lexicon made of multiple sublex-ica where each sublexicon represents entries from a particular tier a rewrite rulessystem that maps multiple lexical representations to a surface representation and amorphotactic component that makes use of regular rewrite rules Rules and lexicaare compiled algorithmically into multitape nite-state machines There is no reasonto believe that our multitiered rewrite rules component cannot be applied to otherrewrite rules systems (Koskenniemi 1983 Kaplan and Kay 1994 Mohri and Sproat1996 Karttunen 1997)

It was demonstrated that the proposed framework is capable of modeling sophis-ticated linguistic descriptions especially those of autosegmental phonology Havingsaid that considering that the morphology of Semitic languages is notoriously dif-cult to analyzemdashpartly because of its root-and-pattern nature and the existence ofmany morphologically distinct homographic morphemes but mostly because the or-thographic system is underspecied (see Section 54)mdashthe current work as well as allreported work on Semitic morphology is far from providing a usable morphologicalsystem Much work in the area of morphological disambiguation which must ventureinto the realms of syntax and semantics awaits research

The proposed multitape approach may not be conned to Semitic and may proveuseful for autosegmental representation in general Since a segment in modern phono-logical theory is a mere shorthand for multitiered features the model may be appliedto concatenative languages when descriptions are required at the multitiered featurelevel While this may be cumbersome for morphological applications it may proveuseful for automatic speech recognition and other applications that require subseg-mental analyses

Acknowledgments

This research was supported by a St Johnrsquos Benefactorsrsquo scholarship and was carriedout under the supervision of Dr Stephen Pulman (University of Cambridge) Thanksare due to the Master and Fellows of St Johnrsquos College and the Computer Labora-tory Cambridge for various grants Much revision and enhancement took place atBell Laboratories Comments by the anonymous reviewers helped in reshaping thepresentation of this paper Ken Beesley kindly made a forthcoming paper availableto me and answered many questions Martin Jansche performed the test detailed inAppendix B2 and provided comments Christine Nakatani provided many useful ed-itorial comments

Appendix A Implementation

The algorithms in Section 4 were implemented by the author in SICStus Prolog us-ing a nite-state library provided by E Grimley-Evans The library allows the cre-ation manipulation and destruction of multitape nite-state machines with an easyalgebraic interface to n-way regular expressions The Prolog term

constructs the machine for the ex-tended regular expression eg expression 3 (Section 421) is turned into afour-tape machine with the expression

The predicate denotes a terminal tuple inx denotes concatena-tion postx denotes Kleene star and a list denotes union over its elements Primi-

99


tive Prolog procedures (eg etc) are also provided for (Kiraz andGrimley-Evans 1998)

The algorithms given in Section 4 are closely followed First the lexical compileris invoked creating a multitape machine for each sublexicon and then putting themtogether with the cross product operator The rule compiler then compiles all therules into another machine The entire language description is then created with theoperation

Language s Lexicon Rules 23

where s denotes the set of all surface symbols The rst component maps the lexiconto all surface symbols The intersection leaves Language with the valid expressionsonly (One can also use composition instead of intersection depending on the natureof the rules)

There is some room to enhance the implementation especially in time and memoryoverhead While the nite-state library is capable of handling automata for small-scalegrammars larger grammars would stretch its capabilities The library was successfullyused however to implement the algorithms in the current work as well as thosepresented by Grimley-Evans (1997) and Kiraz (1997a) It must be stressed that thenite-state calculus library as well as the rule and lexicon compilers are prototypeimplementations written for research purposes An interpreter version of the workpresented here was described earlier (Kiraz 1996) The interpreter works on rulesdirectly and can handle larger grammars

Appendix B Beesleyrsquos Bracketing Algorithm vs Kirazrsquos Multitape Algorithm

B1 Using Bell Labsrsquo LextoolsThis test was performed using the Lextools lexical compiler Each line in the inputle is an extended regular expression The compiler turns each line into an FSA thentakes the union of all FSAs The le may contain a header surrounded between two

s for alias denitions In Beesleyrsquos case the following source le was used (onlytwo roots and two vocalisms are shown)

Each line in the header consists of followed by followed by an extendedregular expression The compiler builds an FSA for the expression and stores it under

In regular expressions curly brackets are used to denote multicharacter symbols(eg ) or special symbols (eg and which otherwise are used for weightsin weighted FSAs) The operators are for subtraction for union for insert orignore for intersection and for reference to a machine already dened inthe header

The implementation of the Lextools insert operator was modied to provide for afair representation of Beesleyrsquos method The initial runs took quite some time (many

100


hours for 100 roots) since the insert operator was initially implemented by the ex-pression Range A B for inserting B into A (Kaplan and Kay 1994) The newalgorithm inserts B directly into A by iterating over states and adding new statesand arcs Additionally since Beesleyrsquos algorithm makes heavy use of alias denitionsaccess to them was enhanced by applying a binary search mechanism rather thanLextoolsrsquos original linear search

For Kirazrsquos method two source les were used The root le is simply a list of allroots eg

and the pattern le is a listing of all vocalisms eg

The two FSAs generated from the two les were fed into a regular expression compilerto compute expression (2) (Section 41)

Table 3 (Section 62) shows the times spent on compiling up to 3000 roots withthe 24 patterns described in (Beesley forthcoming) The test was performed on a MIPSR5000 180MHz based Unix system with a memory size of 64 MB

Caveat is required here To the disadvantage of Kiraz the two FSAs resultingfrom the root and vocalism les are saved on disk then loaded again by the regularexpression compiler to compute their cross product adding unnecessary expensiveIO operations Otherwise the results would be even more in favor of the multitieredmodel

B2 Using van Noordrsquos FSA Utilities (by Martin Jansche)An independent comparison between the approach described here and the one in(Beesley forthcoming) was carried out using van Noordrsquos FSA Utilities (van Noord1997) (we use its notation for regular expressions throughout this section) We com-pared the time spent on compiling lexica of various sizes for both frameworks Givena set of roots and a set of patterns each compiled into a nite automaton as outlinedin Section 41 the key difference between the work of Kiraz and that of Beesley is thatthe former uses the cross product operation to compile the full lexicon while the latteruses intersection Since these two operations are very similar one would not expectmuch of a difference if the elements in each sublexicon were the same However thedifferent formal renderings of roots and patterns in the two approaches results in asignicant difference

Beesley Kiraz

lexicon by intersection cross productroot egpattern eg

Using Beesleyrsquos approach directly made the task of compiling the root lexiconintractable for more than 10 roots After modications to Beesleyrsquos versionmdashsuch asintersecting the disjunction of roots with the disjunction of patterns once5 delimiting

5 We realize that since roots do not apply to all patterns but to lexically dened subsets applyingintersection once does not work in practice It was applied here to enhance the performance ofBeesleyrsquos algorithm

101


root consonants with one special symbol only and inserting other symbols only be-tween root consonants rather than at arbitrary positions so that a typical root now hasthe shape where expands to mdashitbecame tractable but was still much slower than the alternative discussed here

Both approaches were implemented as Prolog code and macros on top of the FSAUtilities The two implementations share common code that contains among otherthings a database of roots and patterns in the form

The data represented there are transformed in different ways by the two imple-mentations

There is a common macro that calls a metapredicate liketo nd the rst solutions to a call to and collects all the s

thus obtained into a big disjunction The compilation of the lexicon is then very sim-ple

While the pattern database is shared between the two implementations the mean-ing of within the patterns is different for Kiraz it is just an ordinary symbolbut for Beesley it expands into a marker for a root consonant followed by any othersymbol (the root consonant itself)

Table 3 shows the times (in seconds) spent on compiling full lexica with differentnumbers of roots and the 24 patterns described in (Beesley forthcoming) Each numberis the minimum obtained after several trials with the ldquowalltimerdquo statistics of SICStusProlog 371 running on an Intel Pentium 233 MHz based Linux system

102


ReferencesBat-El O 1989 Phonology and Word Structure

in Modern Hebrew PhD thesis Universityof California at Los Angeles

Bear J 1988 Morphology with two-levelrules and negative rule features InCOLING-88 Papers Presented to the 12thInternational Conference on ComputationalLinguistics volume 1 pages 28ndash31

Beesley K 1990 Finite-state description ofArabic morphology In Proceedings of theSecond Cambridge Conference BilingualComputing in Arabic and English

Beesley K 1991 Computer analysis ofArabic morphology A two-levelapproach with detours In B Comrie andM Eid editors Perspectives on ArabicLinguistics III Papers from the Third AnnualSymposium on Arabic Linguistics JohnBenjamins Amsterdam pages 155ndash72

Beesley K 1996 Arabic nite-statemorphological analysis and generation InCOLING-96 Papers Presented to the 16thInternational Conference on ComputationalLinguistics volume 1 pages 89ndash94

Beesley K 1998a Arabic morphologicalanalysis on the Internet In Proceedings ofthe 6th International Conference andExhibition on Multi-Lingual Computingpages 311ndash10 Cambridge

Beesley K 1998b Arabic morphology usingonly nite-state operations In M Rosnereditor Proceedings of the Workshop onComputational Approaches to SemiticLanguages pages 50ndash57 Montreal

Beesley K 1998c Constraining separatedmorphotactic dependencies in nite-stategrammars In Proceedings of theInternational Workshop on Finite StateMethods in Natural Language Processingpages 118ndash127 Ankara Turkey

Beesley K Forthcoming Arabic stemmorphotactics via nite-state intersectionIn E Benmamoun editor Perspectives onArabic Linguistics XII Papers from theTwelfth Annual Symposium on ArabicLinguistics pages 85ndash100 John BenjaminsAmsterdam

Beesley K T Buckwalter and S Newton1989 Two-level nite-state analysis ofArabic morphology In Proceedings of theSeminar on Bilingual Computing in Arabicand English The Literary and LinguisticComputing Centre Cambridge

Bird S and T Ellison 1992 One-levelphonology Autosegmentalrepresentations and rules as nite-stateautomata Technical Report ResearchPaper EUCCS RT-51 University of

EdinburghBird S and T Ellison 1994 One-level

phonology Computational Linguistics20(1)55ndash90

Chomsky N 1951 Morphophonemics ofmodern Hebrew Masterrsquos thesisUniversity of Pennsylvania Published byGarland Press New York 1979

Chomsky N and M Halle 1968 The SoundPattern of English Harper and Row NewYork

Daciuk J S Mihov B Watson andR Watson 2000 Incremental constructionof minimal acyclic nite-state automataComputational Linguistics 26(1)3ndash16

Elgot C and J Mezei 1965 On relationsdened by generalized nite automataIBM Journal of Research and Development947ndash68

Fischer P 1965 Multi-tape and innite-stateautomatamdashA survey Communications ofthe ACM 8799ndash805

Goldsmith J 1976 Autosegmental PhonologyPhD thesis MIT Published asAutosegmental and Metrical PhonologyOxford 1990

Grimley-Evans E 1997 Approximatingcontext-free grammars with a nite-statecalculus In Proceedings of the 35th AnnualMeeting of the Association for ComputationalLinguistics and 8th Conference of the EuropeanChapter of the Association for ComputationalLinguistics pages 452ndash9 Madrid Spain

Grimley-Evans E G Kiraz and S Pulman1996 Compiling a partition-basedtwo-level formalism In COLING-96Papers Presented to the 16th InternationalConference on Computational Linguisticsvolume 1 pages 454ndash59

Hammond M 1988 Templatic transfer inArabic broken plurals Natural Languageand Linguistic Theory 6247ndash70

Harris Z 1941 Linguistic structure ofHebrew Journal of the American OrientalSociety 62143ndash67

Kaplan R and M Kay 1994 Regularmodels of phonological rule systemsComputational Linguistics 20(3)331ndash78

Karttunen L 1993 Finite-state lexiconcompiler Technical Report XEROX PaloAlto Research Center April

Karttunen L 1997 The replace operator InE Roche and Y Schabes editorsFinite-State Language Processing MIT Presschapter 4 pages 117ndash47

Karttunen L and K Beesley 1992Two-level rule compiler Technical ReportXEROX Palo Alto Research Center

103


Karttunen L R Kaplan and A Zaenen1992 Two-level morphology withcomposition In COLING-92 PapersPresented to the 15th [sic] InternationalConference on Computational Linguisticsvolume 1 pages 141ndash48 Nantes FranceInternational Committee onComputational Linguistics

Kataja L and K Koskenniemi 1988 Finitestate description of Semitic morphologyIn COLING-88 Papers Presented to the 12thInternational Conference on ComputationalLinguistics volume 1 pages 313ndash15

Kay M 1987 Nonconcatenative nite-statemorphology In Proceedings of the ThirdConference of the European Chapter of theAssociation for Computational Linguisticspages 2ndash10

Kay M and R Kaplan 1983 Wordrecognition Unpublished paper The coreideas are published in Kaplan and Kay(1994)

Kiraz G 1994a Lexical Tools to the Syriac NewTestament JSOT Manuals 7 ShefeldAcademic Press

Kiraz G 1994b Multi-tape two-levelmorphology A case study in Semiticnon-linear morphology In COLING-94Papers Presented to the 15th InternationalConference on Computational Linguisticsvolume 1 pages 180ndash86

Kiraz G 1996 S EMH E A generalisedtwo-level system In Proceedings of the 34thAnnual Meeting pages 159ndash66 Associationfor Computational Linguistics

Kiraz G 1997a Compiling regularformalisms with rule features intonite-state automata In Proceedings of the35th Annual Meeting of the Association forComputational Linguistics and 8th Conferenceof the European Chapter of the Association forComputational Linguistics pages 329ndash36

Kiraz G 1997b Lextools 20 Tools fornite-state linguistic analysis TechnicalReport 011334-970625-04TMBellLaboratories

Kiraz G 1997c Linearization of nonlinearlexical representations In J Colemaneditor Proceedings of the Third Meeting of theACL Special Interest Group in ComputationalPhonology pages 57ndash62

Kiraz G In press Computational NonlinearMorphologyWith Emphasis on SemiticLanguages Cambridge University Press

Kiraz G and E Grimley-Evans 1998Multi-tape automata for speech andlanguage systems A Prologimplementation In Derick Wood andSheng Yu editors AutomataImplementation Lecture Notes inComputer Science Number 1436

Springer Verlag pages 87ndash103Kornai A Formal Phonology PhD thesis

Stanford University Published in 1995Kornai A 1991 Formal Phonology Garland

PublishingKoskenniemi K 1983 Two-Level Morphology

PhD thesis University of HelsinkiLavie A A Itai and U Ornan 1990 On

the applicability of two level morphologyto the inection of Hebrew verbs InY Choueka editor Literary and LinguisticComputing 1988 Proceedings of the 15thInternational Conference pages 246ndash60

McCarthy J 1979 Formal Problems in SemiticPhonology and Morphology PhD thesisMIT Cambridge MA

McCarthy J 1981 A prosodic theory ofnonconcatenative morphology LinguisticInquiry 12(3)373ndash418

McCarthy J 1986 OCP effects Geminationand antigemination Linguistic Inquiry17207ndash63

McCarthy J 1993 Template form inprosodic morphology In Stvan L et aleditors Papers from the Third Annual FormalLinguistics Society of Midamerica Conferencepages 187ndash218 Indiana UniversityLinguistics Club Bloomington

McCarthy J and A Prince 1990a Foot andword in prosodic morphology TheArabic broken plural Natural Languageand Linguistic Theory 8209ndash83

McCarthy J and A Prince 1990b Prosodicmorphology and templatic morphologyIn M Eid and J McCarthy editorsPerspectives on Arabic Linguistics II Papersfrom the Second Annual Symposium on ArabicLinguistics John Benjamins Amsterdampages 1ndash54

McCarthy J and A Prince 1995 Prosodicmorphology In J Goldsmith editor TheHandbook of Phonological Theory Blackwellchapter 9 pages 318ndash66

Mohri M and R Sproat 1996 An efcientcompiler for weighted rewrite rules InProceedings of the 34th Annual Meetingpages 231ndash8 Association forComputational Linguistics

Moscati S A Spitaler E Ullendorff andW von Soden 1969 An Introduction to theComparative Grammar of the SemiticLanguages Phonology and Morphology PortaLinguarum Orientalium OttoHarrassowitz Wiesbaden Second edition

Pulleyblank D 1986 Tone in LexicalPhonology Studies in Natural Languageand Linguistic Theory Reidel

Pulman S and M Hepple 1993 Afeature-based formalism for two-levelphonology A description andimplementation Computer Speech and

104


Language 7333ndash58Rabin M and D Scott 1959 Finite

automata and their decision problemsIBM Journal of Research and Development3114ndash25 Reprinted in E Moore editorSequential Machines Addison-WesleyReading MA 1964 pages 63ndash91

Ritchie G A Black G Russell andS Pulman 1992 ComputationalMorphologyPractical Mechanisms for theEnglish Lexicon MIT Press CambridgeMA

Ruessink H 1989 Two level formalismsTechnical Report 5 Utrecht WorkingPapers in NLP

Spencer A 1991 Morphological Theory BasilBlackwell

Sprout R 1992 Morphology and ComputationMIT Press Cambridge MA

Sprout R 1995 Lextools Tools fornite-state linguistic analysis TechnicalReport 11522-951108-10TMBellLaboratories

Sprout R editor 1997 MultilingualText-to-Speech Synthesis The Bell LabsApproach Kluwer Boston MA

van Noord Gertjan 1997 FSA Utilities Atoolbox to manipulate nite-stateautomata In Darrell Raymond DerickWood and Sheng Yu editors AutomataImplementation Lecture Notes inComputer Science Number 1260Springer Verlag pages 87ndash108

Wiebe B 1992 Modelling autosegmentalphonology with multi-tape nite statetransducers Masterrsquos thesis Simon FraserUniversity

105


The rest of this section discusses the importance of nonlinear morphology andoutlines the research objectives of this work

11 Nonlinear MorphologyEarly generative morphophonological theory was mainly based on the linear segmen-tal approach of The Sound Pattern of English (Chomsky and Halle 1968) In the midseventies however linguists had departed from this linear framework to a nonlinearone Goldsmith (1976) working on the phonology of African tone languages pro-posed autosegmental phonology with multitiered representations Goldsmith madeuse of two tiers to describe tone languages one to represent sequences of vowelsand consonants and another to describe tone segments McCarthy (1979) applied au-tosegmental phonology to Semitic root-and-pattern morphology resulting in what isnow known as the theory of nonconcatenative (or nonlinear) morphology as opposedto concatenative morphology McCarthyrsquos ndings have become ubiquitous In factldquoevery aspect of the theory of morphology and morphophonologyrdquo remarks Spencer(1991 134) ldquohas had to be reappraised in one way or another in the wake of [Mc-Carthyrsquos] analysis of Semitic and other languagesrdquo

Spencerrsquos statement could well apply to the theory of computational morphologyTwo-level morphology (Koskenniemi 1983) as well as its predecessor in the work ofKay and Kaplan (1983) is also deeply rooted in the linear concatenative tradition In-deed ldquoif Koskenniemi had been interested in Arabic or Warlpiri rather than Finnishrdquonotes Sproat (1992 206) ldquohis system might have taken on a rather different characterfrom the startrdquo It would prove difcult if not impossible to implement Semitic lan-guages using linguistically motivated theoretical models such as those of McCarthyand others in the eld with traditional two-level morphology

Kay (1987) was the rst computational linguist to make use of McCarthyrsquos nd-ings He proposed that a four-tape nite-state machine as opposed to the traditionaltwo-tape machines of two-level morphology be used to describe the autonomousmorphemes of Arabic Kay devised a system for manipulating the multitape machinealbeit using an ad hoc procedure to control the movements of the machinersquos head(s)We shall build upon Kayrsquos work by providing higher-level lexical and rule formalismsand algorithms for compiling the formalisms into multitape machines eliminating theneed for the ad hoc procedure that controls head movements We shall revisit Kayrsquosapproach in Section 61

Previous work to implement Semitic languages namely Akkadian (Kataja andKoskenniemi 1988) Arabic (Beesley Buckwalter and Newton 1989 Beesley 1990 19911996 1998a 1998b 1998c forthcoming) and Hebrew (Lavie Itai and Ornan 1990)employed traditional two-level morphology with some augmentation to handle thenonlinearity of stems but did not make any use of the then-available theory of non-concatenative morphology The challenge here lies in the fact that two-level morphol-ogy assumes the lexical representation of a surface form to be the concatenation ofthe corresponding lexical morphemes in question To resolve the problem these au-thors (with the exception of Beesleyrsquos work from 1996 on) provided for a simultaneoussearch of various root and afx lexica the result of which served as the lexical tape ofthe two-level system We shall revisit these approaches in Sections 62 and 63

Other publications dealing with Semitic computational morphology are connedto proposals for compiling autosegmental descriptions into automata (Kornai 1991Wiebe 1992 Bird and Ellison 1992) They revolve around encoding autosegmentalrepresentations (by various encoding mechanisms) and providing ways for compilingsuch encodings into nite machines None provide for lexicon and rule formalismsthat can be compiled into their respective encodings or directly into automata No

78













79











80











81





LLC RLC LSC RSC





82


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105













79











80











81





LLC RLC LSC RSC





82


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105











80











81





LLC RLC LSC RSC





82


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105











81





LLC RLC LSC RSC





82


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105





LLC RLC LSC RSC





82


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105


cXR1 X



v X cv R3

where X is a vowel








XR0 X

where X c v


83










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105










A P B S

P S p1 s1

P S p2 s2

P S pn sn



84



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105



Verb P ktob S

P S ne

P S te

P S te un

P S te Ecircan














85





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105





LiW i

W 1



Lexiconn 1

i 1

Li 2





86





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105





Centers C 3




Restrict c LRc

c 4


Restrict c LRc

c 5


87




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105




Restrict (6)

c

LRc



Restrict 7



Coerce LR

8




88






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105






Aps PS

pBs 10






89




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105




CVV








1 1

2 2


ktba

pnq

qrbe

90






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105






v cV R4

where V is a vowel







91




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105




1 p1 s1 sd1 sd1 1 sn1

2 p2 s1 sd2 sd2 1 sn2









92







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105







p k p t p b p 11


r u r i r 12


93




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105




A k A t A b A 13


B u B i B 14


tVCVCXVC 15

where C isktb 16



94





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105





20 497s 064 78 74 39 1940 985s 079 125 156 61 2660 1464s 081 181 257 74 3580 1951s 095 205 381 93 41

100 2403s 113 237 529 108 49200 4852s 139 349 1770 227 78300 1m 1095s 167 425 3877 376 104400 1m 3742s 187 521 6771 563 120500 2m 694s 262 484 11244 792 142

1000 5m 079s 564 5342000 22m 1953s 1020 13133000 2h 5m 3538s 1260 5980




[ktbampCaCaC] 17



95








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105








x C x Gemination C





96








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105








97



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105



C1 V0 C1 C1 V0 C1 19


0 k1 0 t1 b1 20


a C 21


k1 a0 t1 t1 a0 b1 22



7 Implementation



8 Conclusion


98





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105





Acknowledgments






99













100









Beesley Kiraz




101









102






























103






























104












105













100









Beesley Kiraz




101









102






























103






























104












105









Beesley Kiraz




101









102






























103






























104












105









102






























103






























104












105






























103






























104












105






























104












105












105

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