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, є-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. derivations of substrings of length 1 Basic Algorithm of CYK Recognition (2) Digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 Sign -> + | -

5. Number S -> Integer | Real Integer -> Digit | Integer Digit Digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 derivations of substrings of length 1 Unit Rule: rules of the form A  B, where A and B are non-terminals. We can have chains of them in a derivation. Basic Algorithm of CYK Recognition (3)

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

7. Number S -> Integer | Real Real -> Integer Fraction Scale Number does indeed derive 32.5e+1. Basic Algorithm of CYK Recognition (5)

8. є-rules Basic Algorithm of CYK Recognition (6)

9. Rє = { Empty, Scale } sentence: z = z 1 z 2... z n substring of z starting at position i, of length l. s i,l = z i z i+1... z i+l-1 R s i,l : the set of non-terminals deriving the substring s i,l A graphical presentation of substrings Basic Algorithm of CYK Recognition (7)

10. CYK recognition with a grammar in CNF Required restrictions:  Eliminate є-rules and unit rules  Limit the maximum length of RHS of the rule to 2 CNF  No є-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 l i

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 A chart is just a recognition table.

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!