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Left-Corner Grammar Transform and Incremental Parsing

Left-Corner Grammar Transform and Incremental Parsing. Aria Haghighi. Grammar Transform. A CFG G Nonterminals N Terminals T Productions (Rules) P A grammar Transform : G ! G’. Parsing Strategies. Bottom-Up e.g. CKY Top-Down Inefficient and may not terminate

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Left-Corner Grammar Transform and Incremental Parsing

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  1. Left-Corner Grammar TransformandIncremental Parsing Aria Haghighi

  2. Grammar Transform • A CFG G • Nonterminals N • Terminals T • Productions (Rules) P • A grammar Transform • :G !G’

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

  4. Left-Corner’s 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 • …..

  5. 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’

  6. Problem with the old school • It’s a big school!! • Can have exponential Blowup in number of productions • PCFG Estimation • Lots of sparse rules

  7. Select Left-Corner Transform • Left-corner productions L • Add states D-X

  8. Example Transform

  9. 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

  10. Binarizing the Output For Top-Down Rules: (td) For Left-Corner Rules: (lc)

  11. Grammar Sizes

  12. Incremental Parsing

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

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