LINGUISTICA GENERALE E COMPUTAZIONALE

ANALISI SINTATTICA (PARSING)

RECAP: CFG

• Bird et al, ch. 8.3

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

EXAMPLE (CFR LAST WEEK)

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

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

AN EXAMPLE OF TOP-DOWN SEARCH(IN PARALLEL)

RECURSIVE DESCENT IN NLTK

• P. 303: – nltk.RecursiveDescentParser(grammar)– nltk.app.rdparser()

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)

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

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

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

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

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

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

THE PROBLEM WITH LEFT-RECURSION

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

AN EXAMPLE OF BOTTOM-UP SEARCH

SHIFT-REDUCE PARSING

• P. 305– nltk.app.srparser()– ShiftReduceParser(grammar)

TOP-DOWN vs BOTTOM-UP

• TOP-DOWN:– 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

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

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

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

PP ATTACHMENT AMBIGUITY

AMBIGUITY: SOLUTIONS

• Use a PROBABILISTIC GRAMMAR (not covered in this module)

• Use semantics

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

INVARIANTS AND TOP-DOWN PARSING

THE EARLEY ALGORITHM

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)

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

THE CHART: GRAPHICAL REPRESENTATION

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

EXAMPLES

SUCCESS

• The parser has succeeded if entry N+1 of the chart contains the state– S , [0,N]

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

THE ALGORITHM: CENTRAL LOOP

EARLEY ALGORITHM: THE THREE OPERATORS

EXAMPLE, AGAIN

EXAMPLE: BOOK THAT FLIGHT

EXAMPLE: BOOK THAT FLIGHT (II)

EXAMPLE: BOOK THAT FLIGHT (III)

EXAMPLE: BOOK THAT FLIGHT (IV)

CHART PARSING IN NLTK

• 8.4, p. 307 ff

DEPENDENCY PARSING

• 8.5

READINGS

• Bird et al, chapter 8