a direct link between tree-adjoining and context-free tree ...kilian/a-direct-link.pdf · a direct...
TRANSCRIPT
A direct link between Tree-Adjoining andContext-Free Tree Grammars
Kilian Gebhardt Johannes Osterholzer
Institute of Theoretical Computer ScienceFaculty of Computer Science
Technische Universitat Dresden
June 23, 2015
1/9
Theorem (Kepser and Rogers, 2011)Let L be a tree language. The following are equivalent:
I L is definable by anon-strict tree adjoining grammar.
I L is definable by amonadic linear context-free tree grammar.
TheoremIf a tree language is definable by a
non-strict tree adjoining grammarthen it is also definable by a
monadic linear context-free tree grammar.
new direct construction:productions resemble shape of elementary trees
2/9
Theorem (Kepser and Rogers, 2011)Let L be a tree language. The following are equivalent:
I L is definable by anon-strict tree adjoining grammar.
I L is definable by amonadic linear context-free tree grammar.
TheoremIf a tree language is definable by a
non-strict tree adjoining grammarthen it is also definable by a
monadic linear context-free tree grammar.
new direct construction:productions resemble shape of elementary trees
2/9
Theorem (Kepser and Rogers, 2011)Let L be a tree language. The following are equivalent:
I L is definable by anon-strict tree adjoining grammar.
I L is definable by amonadic linear context-free tree grammar.
TheoremIf a tree language is definable by a
non-strict tree adjoining grammarthen it is also definable by a
monadic linear context-free tree grammar.
new direct construction:productions resemble shape of elementary trees
2/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗ A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗ A
⇒
A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars
vs.linear monadic
context-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗ A ⇒A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars vs.
linear monadiccontext-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A
⇒
A
x1x2x3→
x3x1x3
AA
x→
x
3/9
(non-strict) treeadjoining grammars vs.
linear monadiccontext-free tree grammars
A
︸ ︷︷ ︸n arguments
⇒B
B∗
A
⇒
A
x1x2x3→
x3x1x3
AA
x→
x
3/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
xi xi
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
xi xi
4/9
equivalence proof by Kepser and Rogers
lm-cftg
lnm-cftg
spinal-formed cftg
collapse-freelnm-cftg
footed cftg
(ns)tag
Ax →
Ax → x
Ax→ σ
x
A
x1 xi xk→ σ
x1 xi xk
A
x→
B...
C
x
+σ
D x γ
xi xi
4/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . .
⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
x
D∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
x
D∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
x
D∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
x
D∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . .
⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
A· · ·
⇒B· · ·
⇒ . . . ⇒
...
D· · ·
I order of siblings unaffected
I conceive siblings as 1argument
I plug parent node on top
B∗
LA,DM
x→ LB,DM
xD∗
LD,DM
x→ x
LA,DM
D· · ·
⇒ LB,DM
D· · ·
⇒ . . . ⇒
...
LD,DM
D· · ·
⇒
...
D· · ·
5/9
I: b
1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b
=⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b
=⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2:
a
b a
b∗ b
b =⇒
a
a a
b a
=⇒
a
a a
b a
b
b a
b
yield language: w b w for w ∈ {a,b}∗
6/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,
b
b
b,b
x→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,
b
b
b,b
x→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x
→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a
,a
a
a
,a
a
a
,b
b
b
,b
x
a
,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a
,b
b
b
,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b
,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
I: b 1:
a
a a
b∗ a
2 :
a
b a
b∗ b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
a,a
x→ x
a,a
x→ x
b,b
x→ x
b,b
x→ x
guessing:one-state nondeterministic top-down tree transducer
7/9
S
⇒b,b
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒
a,a
a
a,a
a
a,b
b
b,b
b
a,a
a
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒
a,a
a
a,a
a
a,b
b
b,b
b
a,a
a
⇒∗
a
a a,b
b
b a
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
⇒
a
a a,a
a
b,b
b
a,a
a
b,b
b
b a
b,b
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
⇒
a
a a,a
a
b,b
b
a,a
a
b,b
b
b a
b,b
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
⇒∗
a
a a
b a,a
a
b
b a
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
⇒∗
a
a a
b a,a
a
b
b a
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
S ⇒b,b
b⇒∗
a
a a,b
b
b a
⇒∗
a
a a
b a
b
b a
b
S →b,b
b
b,b
x→
a,a
a
a,a
a
a,b
b
b,b
x
a,a
a
a,b
x→
a,a
a
b,b
b
a,a
a
b,b
x
b,b
b
8/9
conclusions
(non-strict) tree adjoining grammars andlinear monadic context-free tree grammars are equivalent
new construction: nstag to l(n)m-cftgdirect and productions resemble shape of elementary trees
bibliography
S. Kepser and J. Rogers. 2011.The Equivalence of Tree Adjoining Grammars and MonadicLinear Context-Free Tree Grammars.Journal of Logic, Language and Information,20(3):361–384.
A. Fujiyoshi and T. Kasai. 2000.Spinal-Formed Context-Free Tree Grammars.Theory of Computing Systems, 33(1):59–83.
9/9
conclusions
(non-strict) tree adjoining grammars andlinear monadic context-free tree grammars are equivalent
new construction: nstag to l(n)m-cftgdirect and productions resemble shape of elementary trees
bibliography
S. Kepser and J. Rogers. 2011.The Equivalence of Tree Adjoining Grammars and MonadicLinear Context-Free Tree Grammars.Journal of Logic, Language and Information,20(3):361–384.
A. Fujiyoshi and T. Kasai. 2000.Spinal-Formed Context-Free Tree Grammars.Theory of Computing Systems, 33(1):59–83.
9/9
conclusions
(non-strict) tree adjoining grammars andlinear monadic context-free tree grammars are equivalent
new construction: nstag to l(n)m-cftgdirect and productions resemble shape of elementary trees
bibliography
S. Kepser and J. Rogers. 2011.The Equivalence of Tree Adjoining Grammars and MonadicLinear Context-Free Tree Grammars.Journal of Logic, Language and Information,20(3):361–384.
A. Fujiyoshi and T. Kasai. 2000.Spinal-Formed Context-Free Tree Grammars.Theory of Computing Systems, 33(1):59–83.
9/9