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The CYK Parsing Method

Overview. CYK Recognition with CF grammarBasic AlgorithmProblems: unit-rules, ?-rules Recognition with a grammar in CNFCYK Parsing with CNFParsing with CNFRecognition TableChart ParsingSummaryAdvantages and DisadvantagesOther remarks. Basic Algorithm of CYK Recognition (1). Example Gramma

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The CYK Parsing Method

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    1. The CYK Parsing Method Chiyo Hotani Tanya Petrova CL2 Parsing Course 28 November, 2007

    2. Overview CYK Recognition with CF grammar Basic Algorithm Problems: unit-rules, ?-rules Recognition with a grammar in CNF CYK Parsing with CNF Parsing with CNF Recognition Table Chart Parsing Summary Advantages and Disadvantages Other remarks

    3. Basic Algorithm of CYK Recognition (1) Example Grammar: A grammar describing numbers in scientific notation Input: 32.5e+1

    4. Basic Algorithm of CYK Recognition (2)

    5. NumberS -> Integer | Real Integer -> Digit | Integer Digit Digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Basic Algorithm of CYK Recognition (3)

    6. NumberS -> Integer | Real Integer -> Digit | Integer Digit Fraction -> . Integer Scale -> e Sign Integer | Empty Basic Algorithm of CYK Recognition (4)

    7. NumberS -> Integer | Real Real -> Integer Fraction Scale Basic Algorithm of CYK Recognition (5)

    8. Basic Algorithm of CYK Recognition (6)

    9. R? = { Empty, Scale } sentence: z = z1 z2 . . . zn substring of z starting at position i, of length l. si,l = zizi+1. . . zi+l-1 Rsi,l: the set of non-terminals deriving the substring si,l Basic Algorithm of CYK Recognition (7)

    10. CYK recognition with a grammar in CNF Required restrictions: Eliminate ?-rules and unit rules Limit the maximum length of RHS of the rule to 2 CNF No ?-rules and unit rules all rules have one of the following two forms: A?a A?BC

    11. Our example grammar in CNF

    12. CYK Parsing with CNF Building the recognition table Input : Our example grammar in CNF input sentence: 32.5 e + 1

    13. CYK Parsing with the CNF bottom-row : read directly from the grammar (rules of the form A? a )

    14. Two Ways to Copmute a R s i,l: check each right-hand side compute possible right-hand sides from the recognition table

    15. How this is done Example: 2.5 e ( = s 2, 4) 1) N1 not in R s 2, 1 or R s 2, 2 N1 is a member of R s 2, 3 But Scale´ is not a member of R s 5, 1 2) R s 2, 4 is the set of Non- Terminals that have a right-hand side AB where either: A in R s 2, 1 and B in R s 3, 3 A in R s 2, 2 and B in R s 4, 2 A in R s 2, 3 and B in R s 5, 1 Possible combinations: N1 T2 or Number T2 In our grammar we do not have such a right-hand side, so nothing is added to R s 2, 4.

    16. Recognition table

    17. As a result we find out that: This process is much less complicated than the one we saw before

    18. Reasons We do not have to repeat the process again and again until no new Non-Terminals are added to R s i,l (The substrings we are dealing with are really substrings and cannot be equal to the string we start with) We only have to find one place where the substring must be split into two A ? B C Here !

    19. Chart Parsing

    20. A short retrospective of CYK First: recognition table using the original grammar. Then: transforming grammar to CNF.

    21. A short retrospective of CYK cont. CNF is useful for improving the efficiency, but it is actually a bit too restrictive  Disadvantage of CNF: Resulting recognition table lacks the information we need to construct a derivation using the original grammar!

    22. A short retrospective of CYK cont. In the transformation process, some non-terminals were thrown away (non-productive) Missing information could be added.

    23. A short retrospective of CYK cont. Result: almost the same recognition table. Extra information on non-terminals Obtained in a simpler and much more efficient way.

    24. Thank you for your attention! ?

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