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THE CYK PARSING METHOD (2)

THE CYK PARSING METHOD (2). Cornelia Kempa Carla Parra Escartín WS 2006-2007. AGENDA. Building the recognition table Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation

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THE CYK PARSING METHOD (2)

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  1. THE CYK PARSING METHOD (2) Cornelia Kempa Carla Parra Escartín WS 2006-2007

  2. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  3. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  4. 2. Undoing the effect of the CNF transformation 2.1. Overview (1) Tübingen, 4th December 2006

  5. 2. Undoing the effect of the CNF transformation 2.1. Overview (2) Tübingen, 4th December 2006

  6. 2. Undoing the effect of the CNF transformation 2.1. Overview (3) Tübingen, 4th December 2006

  7. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  8. 2. Undoing the effect of the CNF transformation 2.2. Adding removed elements (1) Tübingen, 4th December 2006

  9. 2. Undoing the effect of the CNF transformation 2.2. Adding removed elements (2) • CYK does not require all non-terminals reachable. + Rule added!!! Tübingen, 4th December 2006

  10. 2. Undoing the effect of the CNF transformation 2.2. Adding removed elements (3) New line Tübingen, 4th December 2006

  11. 2. Undoing the effect of the CNF transformation 2.2. Adding removed elements (4) • Set Rsi, 0  non-terminals that can be considered as possibly occurring just in front of symbol zi • Set Rsn +1,0 non-terminals that can occur at the end of the sentence. Tübingen, 4th December 2006

  12. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  13. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.1. Methodology (1) • Derivation starts with start-symbol S. • Is A1A2···Am a right hand side of S? • Does A1A2···Am derive S1,n? • We check this starting with A1 • 2 cases: Tübingen, 4th December 2006

  14. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.1. Methodology (2) A) A1 is a terminal symbol  it must be the first symbol of s1,n  then check if A2···Am derives s2,n-1 B) A1 is a non-terminal symbol  it must be a member of Rs1,k  then check if A2···Am derives s2,k+1,n-k Tübingen, 4th December 2006

  15. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.1. Methodology (3) • Now: determined whether the rule is applicable  if so, which parts of the rule derive which substrings.  Next step: determine how the substrings can be derived. Tübingen, 4th December 2006

  16. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  17. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.2. Left-most derivation (1) Tübingen, 4th December 2006

  18. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.2. Left-most derivation (2) Tübingen, 4th December 2006

  19. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.2. Left-most derivation (3) This is what we saw so far: If we continue... The derivation is: Tübingen, 4th December 2006

  20. 2. Undoing the effect of the CNF transformation 2.3. Parsing2.3.2. Left-most derivation (4) Tübingen, 4th December 2006

  21. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  22. 3. A short retrospective of CYK (1) • First: recognition table using the original grammar. • Then: transforming grammar to CNF. Tübingen, 4th December 2006

  23. 3. A short retrospective of CYK (2) • For efficiency, CNF is a bit too restrictive • Disadvantage of CNF: • Resulting recognition table lacks the information we need to construct a derivation using the original grammar! Tübingen, 4th December 2006

  24. 3. A short retrospective of CYK (3) • In the transformation process, some non-terminals were thrown away (non-productive) • Missing information could be added. Tübingen, 4th December 2006

  25. 3. A short retrospective of CYK (2) • Result: almost the same recognition table. • Extra information on non-terminals • Obtained in a simpler and much more efficient way. Tübingen, 4th December 2006

  26. AGENDA • Building the recognition table • Undoing the effect of the CNF transformation 2.1. Overview 2.2. Adding removed elements 2.3. Parsing 2.3.1. Methodology 2.3.2. Left-most derivation • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  27. 4. Chart parsing (1) • CYK algorithm also known as chart parsing. • Both techniques  variants (some of them identical among the techniques) • Difference: implementation. Tübingen, 4th December 2006

  28. 4. Chart parsing (2) A chart is just a recognition table. Tübingen, 4th December 2006

  29. FINAL OVERVIEW (1) • Building the recognition table • Possible Derivations • Undoing the effect of the CNF transformation. • A short retrospective of CYK • Chart Parsing Tübingen, 4th December 2006

  30. FINAL OVERVIEW (2) Tübingen, 4th December 2006

  31. THANK YOU VERY MUCH

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