LeftCorner Grammar Transform and Incremental Parsing

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Left-Corner Grammar TransformandIncremental
Parsing

• Aria Haghighi

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Grammar Transform

• A CFG G
• Nonterminals N
• Terminals T
• Productions (Rules) P
• A grammar Transform
• G ! G

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Parsing Strategies

• Bottom-Up
• e.g. CKY
• Top-Down
• Inefficient and may not terminate
• Left-Corner
• Recognize Left-Child predict parent

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Left-Corners Arch-Nemesis

• Left recursion
• X ! X ?
• Nontermination
• Recognize X starting at position 1
• Recognize X starting at position 1
• Recognize X starting at position 1
• Recognize X starting at position 1
• ..

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Old School Left-Recursion Removal

• Due to Hopcraft and Ullman
• For
• A ! ?1 ?m (?i ? A ?)
• A ! A ?1 A ?k (?i ? ?)
• Add
• A ! ?1 ?1 A?m ?m A
• A ! ?1 ?1 A . ?k ?k A

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Problem with the old school

• Its a big school!!
• Can have exponential
• Blowup in number of productions
• PCFG Estimation
• Lots of sparse rules

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Select Left-Corner Transform

• Left-corner productions L
• Add states D-X

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Example Transform
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Keeping it Small

• Do we need each D-X ?
• Only if D !L X ?
• How do we choose L ?
• Need all left recursive rules
• Suffice to have rules where
• first child is a non-terminal

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Binarizing the Output
For Top-Down Rules (td)
For Left-Corner Rules (lc)
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Grammar Sizes
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Incremental Parsing
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Incremental Parsing

• Operate on flattened selective left-corner
  algorithm
• Partial Parses include left-chain with heuristic
  filtering
• Beam Search