lecture parsing

7/31/2019 Lecture Parsing

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PARSING WITHCONTEXT-FREE GRAMMARS

- by FaaDoOEngineers.com


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PARSING

Parsing is the process of recognizing and

assigning STRUCTURE Parsing a string with a CFG:

Finding a derivation of the string consistent withthe grammar

The derivation gives us a PARSE TREE



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EXAMPLE (CFR LAST WEEK)



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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 bean analysis of the input

DATA-DRIVEN parsing



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AN EXAMPLE OF TOP-DOWN SEARCH

(IN PARALLEL)



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AN EXAMPLE OF BOTTOM-UP

SEARCH



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TOP-DOWN, DEPTH-FIRST,

LEFT-TO-RIGHT



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LEFT-TO-RIGHT (III)



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LEFT-TO-RIGHT (IV)



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A T-D, D-F, L-R PARSER



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TOP-DOWN vs BOTTOM-UP

TOP-DOWN: Only search among grammatical answers

BUT: suggests hypotheses that may not beconsistent with data

Problem: left-recursion

BOTTOM-UP: Only forms hypotheses consistent with data

BUT: may suggest hypotheses that make nosense globally



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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

DetNPs



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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



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LEFT-CORNER PARSING

A hybrid of top-down and bottom-up parsing

Strategy: dont consider any expansionunless the current input can serve as theLEFT-CORNER of that expansion



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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



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PP ATTACHMENT AMBIGUITY



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INVARIANTS AND TOP-DOWN

PARSING



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DYNAMIC PROGRAMMING

A standard T-D parser would reanalyze AFLIGHT 4 times, always in the same way

A DYNAMIC PROGRAMMING algorithmuses a table (the CHART) to avoid repeatingwork

The Earley algorithm also Does not suffer from the left-recursion problem

Solves an exponential problem in O(n3)



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THE CHART

The Earley algorithm uses a table (the CHART) ofsize 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 thesame way as STATES



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THE CHART:

GRAPHICAL REPRESENTATION



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STATES

A state encodes two types of information: 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



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EXAMPLES



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SUCCESS

The parser has succeeded if entry N+1 of thechart contains the state

S, [0,N]



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EXAMPLE:

BOOK THAT FLIGHT



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EXAMPLE:

BOOK THAT FLIGHT (II)



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EXAMPLE:

BOOK THAT FLIGHT (IV)



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