1. CSA2050 Introduction to Computational Linguistics
Parsing II

2. Problems with Recursive Descent Parsing
Left Recursion
Inefficiency
Repeated Work
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CSA Parsing II

3. Left Recursion
A grammar is left recursive if it contains at least one non-terminal A for which A * A and  * 
(n.b. * is the transitive closure of )
Intuitive idea: derivation of that category includes itself along its leftmost branch. NP  NP PP NP  NP and NP NP  DetP Nominal DetP  NP ' s
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CSA Parsing II

4. Left Recursion Left recursion can lead to an infinite loop [nltk demo
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CSA Parsing II

5. Dealing with Left Recursion
Use different parsing strategy
Reformulate the grammar to eliminate LR
A  A | 
is rewritten as
A  A' A'  A' | 
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CSA Parsing II

6. Rewriting the Grammar NP → NP ‘and’ NP NP → D N | D N PP apr 2008
CSA Parsing II

7. Rewriting the Grammar NP → NP ‘and’ NP β NP → D N | D N PP α apr 2008
CSA Parsing II

8. Rewriting the Grammar NP → NP ‘and’ NP β NP → D N | D N PP α
New Grammar
NP → α NP1
NP1 → β NP1 | ε
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CSA Parsing II

9. Rewriting the Grammar NP → NP ‘and’ NP β NP → D N | D N PP α
New Grammar
NP → α NP1
NP1 → β NP1 | ε
α → D N | D N PP
β → ‘and’ NP
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CSA Parsing II

10. New Parse Tree NP α
NP1
D N
the cat ε
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CSA Parsing II

11. Rewriting the Grammar Different parse tree Unnatural parse tree?
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CSA Parsing II

12. Problems with Recursive Descent Parsing
Left Recursion
Inefficiency
Repeated Work
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CSA Parsing II

13. Inefficiency Top down strategy uses the grammar to predict the input.
Recursive descent cannot confirm a structure until it looks at the input.
Consequently it wastes a lot of time building structures that may be inconsistent with the input.
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CSA Parsing II

14. Prediction can be inefficient
N -> apple
N -> ant
N -> alloy .
N -> zebra
N -> zoo NP
D N
the zoo
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CSA Parsing II

15. Prediction can be inefficient
1. VP -> V NP
2. VP -> V NP PP
The first NP constituent is built by the first rule, which fails.
The same constituents are rebuilt when the parser backtracks to the second rule VP NP
V D N
saw the man with the dog
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CSA Parsing II

16. Problems with Recursive Descent Parsing
Left Recursion
Inefficiency
Repeated Work
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CSA Parsing II

17. Repeated Parsing of Subtrees
a flight 4
from Indianapolis 3
to Houston 2
on TWA 1
A flight from Indianapolis
A flight from Indianapolis to Houston
A flight from Indianapolis to Houston on TWA
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CSA Parsing II

18. Bottom Up Shift/Reduce Algorithm
Two data structures
input string
stack
Repeat until input is exhausted
Shift word to stack
Reduce stack using grammar and lexicon until no further reductions are possible
Unlike top down, algorithm does not require category to be specified in advance. It simply finds all possible trees.
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CSA Parsing II

19. Shift/Reduce Operation→|
Step Action Stack Input
0 (start) the dog barked
1 shift the dog barked
2 reduce d dog barked
3 shift dog d barked
4 reduce n d barked
5 reduce np barked
6 shift barked np
7 reduce v np
8 reduce vp np
9 reduce s
>>>from nltk.draw.srparser import demo
>>>srparser.demo()
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CSA Parsing II

20. Shift Reduce Parser
Standard implementations do not perform backtracking (e.g. NLTK)
Only one result is returned even when sentence is ambiguous.
May not fail even when sentence is grammatical
Shift/Reduce conflict
Reduce/Reduce conflict
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CSA Parsing II

21. Handling Conflicts
Shift-reduce parsers may employ policies for resolving such conflicts, e.g.
For Shift/Reduce Conflicts
Prefer shift
Prefer reduce
For Reduce/Reduce Conflicts
Choose reduction which removes most elements from the stack
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CSA Parsing II

22. Top Down vs Bottom Up General
For: Never wastes time exploring trees that cannot be derived from S
Against: Can generate trees that are not consistent with the input
Bottom up
For: Never wastes time building trees that cannot lead to input text segments.
Against: Can generate subtrees that can never lead to an S node.
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CSA Parsing II

23. Top Down Parsing - Remarks
Top-down parsers do well if there is useful grammar driven control: search can be directed by the grammar.
Not too many different rules for the same category
Not too much distance between non terminal and terminal categories.
Top-down is unsuitable for rewriting parts of speech (preterminals) with words (terminals). In practice that is always done bottom-up as lexical lookup.
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CSA Parsing II

24. Bottom Up Parsing - Remarks
It is data-directed: it attempts to parse the words that are there.
Does well, e.g. for lexical lookup.
Does badly if there are many rules with similar RHS categories.
Inefficient when there is great lexical ambiguity (grammar driven control might help here)
Empty categories: termination problem unless rewriting of empty constituents is somehow restricted (but then it’s generally incomplete)
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CSA Parsing II

25. Left Corner Parsing S → NP VP NP → D N NP → D N PP NP → PN
… more rules
D → the
D → a
PN → John
“John saw the dog”
There are three NP rules
If you were parsing top down, which NP rule will be used first?
Is this the best?
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CSA Parsing II

26. Left Corner Parsing
We know that parser has to expand NP in such a way that NP derives “John”.
There is only one rule which does this.
Basic idea behind Left Corner parser is to use input to determine which rule is most relevant.
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CSA Parsing II

27. Bottom Up Filtering
We know the current input word must serve as the first word in the derivation of the unexpanded node the parser is currently processing.
Therefore the parser should not consider grammar rule for which the current word cannot serve as the "left corner"
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28. Left Corner The node marked Verb is a left corner of VP fl fl apr 2008
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29. Left Corner Definition
X is a direct left corner of a nonterminal A, if there is an A-production with X as the left-most symbol on the right-hand side.
the left-corner relation is the reflexive transitive closure of the direct-left-corner relation.
proper-left-corner relation is the transitive closure of the direct-left-corner relation.
Proper left corners of all non-terminal categories can be determined in advance and placed in a table.
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CSA Parsing II

30. DCG-style Grammar/Lexicon
s --> np, vp.
s --> aux, np, vp.
s --> vp.
np --> det nom.
nom --> noun.
nom --> noun, nom.
nom --> nom, pp
pp --> prep, np.
np --> pn.
vp --> v.
vp --> v np
What are the left corners of S?
What are the proper left corners of S?
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CSA Parsing II

31. DCG-style Grammar/Lexicon
s --> np, vp.
s --> aux, np, vp.
s --> vp.
np --> det nom.
nom --> noun.
nom --> noun, nom.
nom --> nom, pp
pp --> prep, np.
np --> pn.
vp --> v.
vp --> v np
What are the left corners of S?
np, aux, vp, det, pn, noun, v
What are the proper left corners of S?
s, np, aux, vp, det, pn, noun, v
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32. Example of Left Corner Table
Category
Proper Left Corners s np
nom vp
np, aux, vp, det, pn, noun, v
pn, det
noun v
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CSA Parsing II

33. How to use the Left Corner Table
If attempting to parse category A, only consider rules A → Bα for which category(current input)  LeftCorners(B)
s → np vp s → aux np vp s → vp
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34. Left Corner Parsing Algorithm
Key Idea: accept a word, identify the constituent it marks the beginning of, and parse the rest of the constituent top down.
Main Advantages:
Like a bottom-up parser, can handle left recursion without looping, since it starts each constituent by accepting a word from the input string.
Like a top-down parser, is always expecting a particular category for which only a few of the grammar rules are relevant. It is therefore more efficient than a plain shift-reduce algorithm.
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35. Left Corner Algorithm define parse(C) //parse a constituent of type C:
{ W = readnextword()
K = category(w)
complete(K,C) }
define complete(K,C)
{ if K=C, exit with success
else
foreach rule (CC -> K α)  Grammar
{ parseList(α);
complete(CC,C)}
define parselist(L)
{if empty(L) succeed
else { parse(head(L)); parselist(tail(L)) }
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CSA Parsing II

36. Left Corner Example Input: Vincent slept; parse s (top down) S
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

37. Left Corner Example Category of next input word = pn (bottom up) pn
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

38. Left Corner Example select rule with direct left corner = pn np → pn
parse remainder of rhs (nothing remains) np pn
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

39. Left Corner Example select rule with direct left corner = np s → np vp
parse remainder of rhs = [ vp ] np pn
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

40. Left Corner Example Category of next input word = iv (bottom up) np
pn iv
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

41. Left Corner Example Select rule with direct left corner = iv vp → iv
parse remainder of rhs. nothing left so
np vp
pn iv
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II

42. Left Corner Example with vp complete, nothing left on rhs of s rule s
np vp
pn iv
Vincent slept
s → np vp
np → d n
np → pn
vp → iv
d → the
n → robber
pn → vincent
iv → slept
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CSA Parsing II