Parsing

1
Parsing

• SLP Chapter 13

2
Outline

• Parsing with CFGs
• Bottom-up, top-down
• CKY parsing
• Mention of Earley and chart parsing

3
Parsing

• Parsing with CFGs refers to the task of assigning
  trees to input strings
• Trees that covers all and only the elements of
  the input and has an S at the top
• This chapter find all possible trees
• Next chapter (14) choose the most probable one

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Parsing

• parsing involves a search

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Top-Down Search

• Were trying to find trees rooted with an S
  start with the rules that give us an S.
• Then we can work our way down from there to the
  words.

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Top Down Space
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Bottom-Up Parsing

• We also want trees that cover the input words.
• Start with trees that link up with the words
• Then work your way up from there to larger and
  larger trees.

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Bottom-Up Space
8
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Top-Down and Bottom-Up

• Top-down
• Only searches for trees that can be Ss
• But also suggests trees that are not consistent
  with any of the words
• Bottom-up
• Only forms trees consistent with the words
• But suggests trees that make no sense globally

10
Control

• Which node to try to expand next
• Which grammar rule to use to expand a node
• One approach exhaustive search of the space of
  possibilities
• Not feasible
• Time is exponential in the number of
  non-terminals
• LOTS of repeated work, as the same constituent is
  created over and over (shared sub-problems)

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Dynamic Programming

• DP search methods fill tables with partial
  results and thereby
• Avoid doing avoidable repeated work
• Solve exponential problems in polynomial time
  (well, no not really well return to this
  point)
• Efficiently store ambiguous structures with
  shared sub-parts.
• Well cover two approaches that roughly
  correspond to bottom-up and top-down approaches.
• CKY
• Earley we will mention this, not cover it in
  detail

12
CKY Parsing

• Consider the rule A ? BC
• If there is an A somewhere in the input then
  there must be a B followed by a C in the input.
• If the A spans from i to j in the input then
  there must be some k st. iltkltj
• Ie. The B splits from the C someplace.

13
Convert Grammar to CNF

• What if your grammar isnt binary?
• As in the case of the TreeBank grammar?
• Convert it to binary any arbitrary CFG can be
  rewritten into Chomsky-Normal Form automatically.
• The resulting grammar accepts (and rejects) the
  same set of strings as the original grammar.
• But the resulting derivations (trees) are
  different.
• We saw this in the last set of lecture notes

14
Convert Grammar to CNF

• More specifically, we want our rules to be of the
  form
• A ? B C
• Or
• A ? w
• That is, rules can expand to either 2
  non-terminals or to a single terminal.

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Binarization Intuition

• Introduce new intermediate non-terminals into the
  grammar that distribute rules with length gt 2
  over several rules.
• So S ? A B C turns into
• S ? X C and
• X ? A B
• Where X is a symbol that doesnt occur anywhere
  else in the the grammar.

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Converting grammar to CNF

• Copy all conforming rules to the new grammar
  unchanged
• Convert terminals within rules to dummy
  non-terminals
• Convert unit productions
• Make all rules with NTs on the right binary
• In lecture what these mean apply to example on
  next two slides

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Sample L1 Grammar
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CNF Conversion
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CKY

• Build a table so that an A spanning from i to j
  in the input is placed in cell i,j in the
  table.
• E.g., a non-terminal spanning an entire string
  will sit in cell 0, n
• Hopefully an S

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CKY

• If
• there is an A spanning i,j in the input
• A ? B C is a rule in the grammar
• Then
• There must be a B in i,k and a C in k,j for
  some iltkltj

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CKY

• The loops to fill the table a column at a time,
  from left to right, bottom to top.
• When were filling a cell, the parts needed to
  fill it are already in the table
• to the left and below

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CKY Algorithm
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Example
Go through full example in lecture
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CKY Parsing

• Is that really a parser?
• So, far it is only a recognizer
• Success? an S in cell 0,N
• To turn it into a parser see Lecture

25
CKY Notes

• Since its bottom up, CKY populates the table
  with a lot of worthless constituents.
• To avoid this we can switch to a top-down control
  strategy
• Or we can add some kind of filtering that blocks
  constituents where they can not happen in a final
  analysis.

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Dynamic Programming Parsing Methods

• CKY (Cocke-Kasami-Younger) algorithm based on
  bottom-up parsing and requires first normalizing
  the grammar.
• Earley parser is based on top-down parsing and
  does not require normalizing grammar but is more
  complex.
• More generally, chart parsers retain completed
  phrases in a chart and can combine top-down and
  bottom-up search.

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Conclusions

• Syntax parse trees specify the syntactic
  structure of a sentence that helps determine its
  meaning.
• John ate the spaghetti with meatballs with
  chopsticks.
• How did John eat the spaghetti?
  What did John eat?
• CFGs can be used to define the grammar of a
  natural language.
• Dynamic programming algorithms allow computing a
  single parse tree in cubic time or all parse
  trees in exponential time.