1. PARSING WITH CONTEXT-FREE GRAMMARS
cc437

2. PARSING Parsing is the process of recognizing and assigning STRUCTURE
Parsing a string with a CFG:
Finding a derivation of the string consistent with the grammar
The derivation gives us a PARSE TREE

3. EXAMPLE (CFR LAST WEEK)

4. PARSING AS SEARCH
Just as in the case of non-deterministic regular expressions, the main problem with parsing is the existence of CHOICE POINTS
There is a need for a SEARCH STRATEGY determining the order in which alternatives are considered

5. TOP-DOWN AND BOTTOM-UP SEARCH STRATEGIES
The search has to be guided by the INPUT and the GRAMMAR
TOP-DOWN search: the parse tree has to be rooted in the start symbol S
EXPECTATION-DRIVEN parsing
BOTTOM-UP search: the parse tree must be an analysis of the input
DATA-DRIVEN parsing

6. AN EXAMPLE OF TOP-DOWN SEARCH (IN PARALLEL)

7. AN EXAMPLE OF BOTTOM-UP SEARCH

8. NON-PARALLEL SEARCH
If it’s not possible to examine all alternatives in parallel, it’s necessary to make further decisions:
Which node in the current search space to expand first (breadth-first or depth-first)
Which of the applicable grammar rules to expand first
Which leaf node in a parse tree to expand next (e.g., leftmost)

9. TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT

10. TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (II)

11. TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (III)

12. TOP-DOWN, DEPTH-FIRST, LEFT-TO-RIGHT (IV)

13. A T-D, D-F, L-R PARSER
(Compare with ND-recognize)

14. TOP-DOWN vs BOTTOM-UP TOP-DOWN: BOTTOM-UP:
Only search among grammatical answers
BUT: suggests hypotheses that may not be consistent with data
Problem: left-recursion
BOTTOM-UP:
Only forms hypotheses consistent with data
BUT: may suggest hypotheses that make no sense globally

15. LEFT-RECURSION
A LEFT-RECURSIVE grammar may cause a T-D, D-F, L-R parser to never return
Examples of left-recursive rules:
NP  NP PP
S  S and S
But also:
NP  Det Nom
Det  NP’s

16. THE PROBLEM WITH LEFT-RECURSION

17. LEFT-RECURSION: POOR SOLUTIONS
Rewrite the grammar to a weakly equivalent one
Problem: may not get correct parse tree
Limit the depth during search
Problem: limit is arbitrary

18. LEFT-CORNER PARSING A hybrid of top-down and bottom-up parsing
Strategy: don’t consider any expansion unless the current input can serve as the LEFT-CORNER of that expansion

19. FURTHER PROBLEMS IN PARSING
Ambiguity
Church and Patel (1982): the number of attachment ambiguities grows like the Catalan numbers
C(2) = 2, C(3) = 5, C(4) = 14, C(5) = 132, C(6) = 469, C(7) = 1430, C(8) = 4867
Avoiding reparsing

20. COMMON STRUCTURAL AMBIGUITIES
COORDINATION ambiguity
OLD (MEN AND WOMEN) vs (OLD MEN) AND WOMEN
ATTACHMENT ambiguity:
Gerundive VP attachment ambiguity
I saw the Eiffel Tower flying to Paris
PP attachment ambiguity
I shot an elephant in my pajamas

21. PP ATTACHMENT AMBIGUITY

22. AMBIGUITY: SOLUTIONS
Use a PROBABILISTIC GRAMMAR (not covered in this module)
Use semantics

23. AVOID RECOMPUTING INVARIANTS
Consider parsing with a top-down parser the NP:
A flight from Indianapolis to Houston on TWA
With the grammar rules:
NP  Det Nominal
NP  NP PP
NP  ProperNoun

24. INVARIANTS AND TOP-DOWN PARSING

25. THE EARLEY ALGORITHM

26. DYNAMIC PROGRAMMING
A standard T-D parser would reanalyze A FLIGHT 4 times, always in the same way
A DYNAMIC PROGRAMMING algorithm uses a table (the CHART) to avoid repeating work
The Earley algorithm also
Does not suffer from the left-recursion problem
Solves an exponential problem in O(n3)

27. THE CHART
The Earley algorithm uses a table (the CHART) of size N+1, where N is the length of the input
Table entries sit in the `gaps’ between words
Each entry in the chart is a list of
Completed constituents
In-progress constituents
Predicted constituents
All three types of objects are represented in the same way as STATES

28. THE CHART: GRAPHICAL REPRESENTATION

29. STATES A state encodes two types of information: DOTTED RULES
How much of a certain rule has been encountered in the input
Which positions are covered
A  , [X,Y]
DOTTED RULES
VP  V NP 
NP  Det  Nominal
S   VP

30. EXAMPLES

31. SUCCESS
The parser has succeeded if entry N+1 of the chart contains the state
S   , [0,N]

32. THE ALGORITHM
The algorithm loops through the input without backtracking, at each step performing three operations:
PREDICTOR: add predictions to the chart
COMPLETER: Move the dot to the right when looked-for constituent is found
SCANNER: read in the next input word

33. THE ALGORITHM: CENTRAL LOOP

34. EARLEY ALGORITHM: THE THREE OPERATORS

35. EXAMPLE, AGAIN

36. EXAMPLE: BOOK THAT FLIGHT

37. EXAMPLE: BOOK THAT FLIGHT (II)

38. EXAMPLE: BOOK THAT FLIGHT (III)

39. EXAMPLE: BOOK THAT FLIGHT (IV)

40. READINGS
Jurafsky and Martin, chapter