PARSING WITH CONTEXTFREE GRAMMARS

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PARSING WITH CONTEXT-FREE GRAMMARS

• James Pustejovsky
• CS 114

Thanks to Massimo Poesio
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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

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EXAMPLE (CFR LAST WEEK)
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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

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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

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AN EXAMPLE OF TOP-DOWN SEARCH(IN PARALLEL)
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AN EXAMPLE OF BOTTOM-UP SEARCH
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NON-PARALLEL SEARCH

• If its not possible to examine all alternatives
  in parallel, its 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)

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TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT
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TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (II)
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TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (III)
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TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (IV)
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A T-D, D-F, L-R PARSER
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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

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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 ? NPs

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THE PROBLEM WITH LEFT-RECURSION
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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

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LEFT-CORNER PARSING

• A hybrid of top-down and bottom-up parsing
• Strategy dont consider any expansion unless the
  current input can serve as the LEFT-CORNER of
  that expansion

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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

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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

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PP ATTACHMENT AMBIGUITY
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AMBIGUITY SOLUTIONS

• Use a PROBABILISTIC GRAMMAR (not covered in this
  module)
• Use semantics

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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

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INVARIANTS AND TOP-DOWN PARSING
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THE EARLEY ALGORITHM

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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)

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THE CHART

• The Earley algorithm uses a table (the CHART) of
  size N1, 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

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THE CHART GRAPHICAL REPRESENTATION
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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

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EXAMPLES
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SUCCESS

• The parser has succeeded if entry N1 of the
  chart contains the state
• S ? ? ?, 0,N

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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

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THE ALGORITHM CENTRAL LOOP
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EARLEY ALGORITHM THE THREE OPERATORS
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EXAMPLE, AGAIN
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EXAMPLE BOOK THAT FLIGHT
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EXAMPLE BOOK THAT FLIGHT (II)
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EXAMPLE BOOK THAT FLIGHT (III)
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EXAMPLE BOOK THAT FLIGHT (IV)
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READINGS

• Jurafsky and Martin, chapter 10.1-10.4