December 2003 CSA3050: Parsing Algorithms 2 1

CSA3050: NLP Algorithms

Parsing Algorithms 2

Problems with DFTD Parser

Earley Parsing Algorithm

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Problems withDFTD Parser

• Left Recursion• Ambiguity• Inefficiency

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Left Recursion

• A grammar is left recursive if it contains at least one non-terminal A for whichA * A and *

• 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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Infinite Search

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Dealing with Left Recursion

• Reformulate the grammar – A A |

as– A A'

A' A' |

– Disadvantage: different (and probably unnatural) parse trees.

• Use a different parse algorithm

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Ambiguity

• Coordination Ambiguity: different scope of conjunction:Black cats and dogs like to play

• Attachment Ambiguity: a constituent can be added to the parse tree in different places:I shot an elephant in my pyjamas

• VP → VP PPNP → NP PP

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Catalan Numbers

The nth Catalan number counts the ways of dissecting a polygon with n+2 sides into triangles by drawing nonintersecting diagonals. No of PPs # parses

2 2

3 5

4 14

5 132

6 469

7 1430

8 4867

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Handling Disambiguation

• Statistical disambiguation

• Semantic knowledge.

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Repeated Parsing ofSubtrees

a flight 4

from Indianapolis 3

to Houston 2

on TWA 1

A flight from Indianapolis 3

A flight from Indianapolis to Houston

2

A flight from Indianapolis to Houston on TWA

1

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Earley Algorithm• Dynamic Programming: solution involves

filling in table of solutions to subproblems.

• Parallel Top Down Search

• Worst case complexity = O(N3) in length N of sentence.

• Table, called a chart, contains N+1 entries

● book ● that ● flight ● 0 1 2 3

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The Chart

• Each table entry contains a list of states• Each state represents all partial parses that have

been reached so far at that point in the sentence.• States are represented using dotted rules

containing information about– Rule/subtree: which rule has been used

– Progress: dot indicates how much of rule's RHS has been recognised.

– Position: text segment to which this parse applies

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Examples of Dotted Rules

• Initial S RuleS → ● VP, [0,0]

• Partially recognised NPNP → Det ● Nominal, [1,2]

• Fully recognised VPVP → V VP ● , [0,3]

• These states can also be represented graphically

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The Chart

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Earley Algorithm

• Main Algorithm: proceeds through each text position, applying one of the three operators below.

• Predictor: Creates "initial states" (ie states whose RHS is completely unparsed).

• Scanner: checks current input when next category to be recognised is pre-terminal.

• Completer: when a state is "complete" (nothing after dot), advance all states to the left that are looking for the associated category.

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Early Algorithm – Main Function

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Early Algorithm – Sub Functions

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fl

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Retrieving Trees• To turn recogniser into a parser, representation of

each state must also include information about completed states that generated its constituents

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Chart[3]

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