parsing with context-free grammars cc437. parsing parsing is the process of recognizing and...
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PARSING WITH CONTEXT-FREE GRAMMARS
cc437
PARSING
Parsing is the process of recognizing and assigning STRUCTURE
Parsing a string with a CFG: – Finding a derivation of the string consistent with
the grammar– The derivation gives us a PARSE TREE
EXAMPLE (CFR LAST WEEK)
PARSING AS SEARCH
Just as in the case of non-deterministic regular expressions, the main problem with parsing is the existence of CHOICE POINTS
There is a need for a SEARCH STRATEGY determining the order in which alternatives are considered
TOP-DOWN AND BOTTOM-UP SEARCH STRATEGIES
The search has to be guided by the INPUT and the GRAMMAR
TOP-DOWN search: the parse tree has to be rooted in the start symbol S– EXPECTATION-DRIVEN parsing
BOTTOM-UP search: the parse tree must be an analysis of the input– DATA-DRIVEN parsing
AN EXAMPLE OF TOP-DOWN SEARCH(IN PARALLEL)
AN EXAMPLE OF BOTTOM-UP SEARCH
NON-PARALLEL SEARCH
If it’s not possible to examine all alternatives in parallel, it’s necessary to make further decisions:– Which node in the current search space to
expand first (breadth-first or depth-first)– Which of the applicable grammar rules to expand
first– Which leaf node in a parse tree to expand next
(e.g., leftmost)
TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT
TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (II)
TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (III)
TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (IV)
A T-D, D-F, L-R PARSER
TOP-DOWN vs BOTTOM-UP
TOP-DOWN:– Only search among grammatical answers– BUT: suggests hypotheses that may not be
consistent with data– Problem: left-recursion
BOTTOM-UP:– Only forms hypotheses consistent with data– BUT: may suggest hypotheses that make no
sense globally
LEFT-RECURSION
A LEFT-RECURSIVE grammar may cause a T-D, D-F, L-R parser to never return
Examples of left-recursive rules:– NP NP PP– S S and S– But also:
NP Det Nom Det NP’s
THE PROBLEM WITH LEFT-RECURSION
LEFT-RECURSION: POOR SOLUTIONS
Rewrite the grammar to a weakly equivalent one– Problem: may not get correct parse tree
Limit the depth during search– Problem: limit is arbitrary
LEFT-CORNER PARSING
A hybrid of top-down and bottom-up parsing Strategy: don’t consider any expansion
unless the current input can serve as the LEFT-CORNER of that expansion
FURTHER PROBLEMS IN PARSING
Ambiguity – Church and Patel (1982): the number of
attachment ambiguities grows like the Catalan numbers
C(2) = 2, C(3) = 5, C(4) = 14, C(5) = 132, C(6) = 469, C(7) = 1430, C(8) = 4867
Avoiding reparsing
COMMON STRUCTURAL AMBIGUITIES
COORDINATION ambiguity– OLD (MEN AND WOMEN) vs
(OLD MEN) AND WOMEN
ATTACHMENT ambiguity:– Gerundive VP attachment ambiguity
I saw the Eiffel Tower flying to Paris
– PP attachment ambiguity I shot an elephant in my pajamas
PP ATTACHMENT AMBIGUITY
AMBIGUITY: SOLUTIONS
Use a PROBABILISTIC GRAMMAR (not covered in this module)
Use semantics
AVOID RECOMPUTING INVARIANTS
Consider parsing with a top-down parser the NP:– A flight from Indianapolis to Houston on TWA
With the grammar rules:– NP Det Nominal– NP NP PP– NP ProperNoun
INVARIANTS AND TOP-DOWN PARSING
THE EARLEY ALGORITHM
DYNAMIC PROGRAMMING
A standard T-D parser would reanalyze A FLIGHT 4 times, always in the same way
A DYNAMIC PROGRAMMING algorithm uses a table (the CHART) to avoid repeating work
The Earley algorithm also– Does not suffer from the left-recursion problem– Solves an exponential problem in O(n3)
THE CHART
The Earley algorithm uses a table (the CHART) of size N+1, where N is the length of the input
– Table entries sit in the `gaps’ between words
Each entry in the chart is a list of – Completed constituents– In-progress constituents– Predicted constituents
All three types of objects are represented in the same way as STATES
THE CHART: GRAPHICAL REPRESENTATION
STATES
A state encodes two types of information:– How much of a certain rule has been encountered
in the input– Which positions are covered– A , [X,Y]
DOTTED RULES– VP V NP – NP Det Nominal– S VP
EXAMPLES
SUCCESS
The parser has succeeded if entry N+1 of the chart contains the state– S , [0,N]
THE ALGORITHM
The algorithm loops through the input without backtracking, at each step performing three operations:– PREDICTOR: add predictions to the chart– COMPLETER: Move the dot to the right when
looked-for constituent is found– SCANNER: read in the next input word
THE ALGORITHM: CENTRAL LOOP
EARLEY ALGORITHM: THE THREE OPERATORS
EXAMPLE, AGAIN
EXAMPLE: BOOK THAT FLIGHT
EXAMPLE: BOOK THAT FLIGHT (II)
EXAMPLE: BOOK THAT FLIGHT (III)
EXAMPLE: BOOK THAT FLIGHT (IV)
READINGS
Jurafsky and Martin, chapter 10.1-10.4