Left-corner parsing Laura Kassner laura.kassner@gmx.de - - PowerPoint PPT Presentation

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Left-corner parsing Laura Kassner laura.kassner@gmx.de - - PowerPoint PPT Presentation

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Left-corner parsing Laura Kassner laura.kassner@gmx.de Computational Linguistics II: Parsing January 10th, 2007 Left-corner parsing Basics Building a left-corner recognizer... ... and transforming it into a parser Comparison to

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Left-corner parsing

Laura Kassner

laura.kassner@gmx.de

Computational Linguistics II: Parsing

January 10th, 2007

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Left-corner parsing

  • Basics
  • Building a left-corner recognizer...
  • ... and transforming it into a parser
  • Comparison to top-down and bottom-up

approaches

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Left-corner parsing: Basics

What is left-corner parsing?

picture taken from Shravan Vasishth's HSP seminar slides

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Left-corner parsing: Basics

  • bottom-up and top-down aspects
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Left-corner parsing: Basics

  • bottom-up and top-down aspects
  • bottom-up: rule k0 -> k1... kn can only be applied

if for every ki (1 <= i <= n), a complete partial structure has been recognized

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Left-corner parsing: Basics

  • bottom-up and top-down aspects
  • bottom-up: rule k0 -> k1... kn can only be applied

if for every ki (1 <= i <= n), a complete partial structure has been recognized

  • left-corner: a structure dominated by k1 must

have been recognized for a rule to be applied

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SLIDE 7

Left-corner parsing: Basics

  • bottom-up and top-down aspects
  • bottom-up: rule k0 -> k1... kn can only be applied

if for every ki (1 <= i <= n), a complete partial structure has been recognized

  • left-corner: a structure dominated by k1 must

have been recognized for a rule to be applied => k1 is “left corner“ of the rule – first symbol on the right hand side

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Left-corner parsing: Basics

  • bottom-up and top-down aspects
  • bottom-up: rule k0 -> k1... kn can only be applied

if for every ki (1 <= i <= n), a complete partial structure has been recognized

  • left-corner: a structure dominated by k1 must

have been recognized for a rule to be applied => k1 is “left corner“ of the rule – first symbol on the right hand side => rule used to make assumptions about the category dominating k1 and about following constituents

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Left-corner parsing: Basics

What is a left-corner parse?

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Left-corner parsing: Basics

What is a left-corner parse?

  • context-free grammar G = <N, T, S, R>
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Left-corner parsing: Basics

What is a left-corner parse?

  • context-free grammar G = <N, T, S, R>
  • string w
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Left-corner parsing: Basics

What is a left-corner parse?

  • context-free grammar G = <N, T, S, R>
  • string w

=> series of rule indices γ = i1 ... in which corresponds to a derivation of string w in G

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Left-corner parsing: Basics

Ordering rules:

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ 2 – nodes in β are ordered the following way:

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ 2 – nodes in β are ordered the following way:

a) if n DD n1 ... nm, all nodes of the subtree with root n1 are in front of n;

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ 2 – nodes in β are ordered the following way:

a) if n DD n1 ... nm, all nodes of the subtree with root n1 are in front of n; b) n is in front of all other nodes it dominates

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ 2 – nodes in β are ordered the following way:

a) if n DD n1 ... nm, all nodes of the subtree with root n1 are in front of n; b) n is in front of all other nodes it dominates c) all nodes dominated by ni are in front of the nodes dominated by ni+1

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Left-corner parsing: Basics

Ordering rules: 1 – β ist the tree structure implied by γ 2 – nodes in β are ordered the following way:

a) if n DD n1 ... nm, all nodes of the subtree with root n1 are in front of n; b) n is in front of all other nodes it dominates c) all nodes dominated by ni are in front of the nodes dominated by ni+1

3 – the order of rule applications described by γ does not violate these rules

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Left-corner parsing: Basics

=> inorder tree traversal!!!

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Left-corner parsing: Basics

An example:

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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab
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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab
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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab

Order of nodes: 4 2 9 5 15 10 16 11 12 6 1 13 7 3 14 8

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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab

Order of nodes: 4 2 9 5 15 10 16 11 12 6 1 13 7 3 14 8 TD parse: 1 3 3 4 4 4 2 6 5

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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab

Order of nodes: 4 2 9 5 15 10 16 11 12 6 1 13 7 3 14 8 TD parse: 1 3 3 4 4 4 2 6 5 BU parse: 4 4 3 4 3 6 5 2 1

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Left-corner parsing: Basics

An example:

  • grammar rules: 1: S -> AS

2: S-> BB 3: A -> bAA 4: A -> a 5: B -> b 6: B -> e

  • sentence: bbaaab

Order of nodes: 4 2 9 5 15 10 16 11 12 6 1 13 7 3 14 8 TD parse: 1 3 3 4 4 4 2 6 5 BU parse: 4 4 3 4 3 6 5 2 1 LC parse: 3 3 4 4 4 1 6 2 5

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Questions?

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Building a left-corner recognizer

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks 1) SENTENCE to be processed

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks 1) SENTENCE to be processed 2) CATEGORIES to be recognized

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks 1) SENTENCE to be processed 2) CATEGORIES to be recognized 3) CONSTITUENTS we are looking for

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks 1) SENTENCE to be processed 2) CATEGORIES to be recognized 3) CONSTITUENTS we are looking for Stack operations:

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Building a left-corner recognizer

Data: CFG <N, T, S, R> Lexicon L Data structures: 3 stacks 1) SENTENCE to be processed 2) CATEGORIES to be recognized 3) CONSTITUENTS we are looking for Stack operations: pop(STACK) push(element, STACK) first(STACK)

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Building a left-corner recognizer

Procedures

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Building a left-corner recognizer

Procedures

REDUCE

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Building a left-corner recognizer

Procedures

REDUCE

Preconditions:

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Building a left-corner recognizer

Procedures

REDUCE

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0

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Building a left-corner recognizer

Procedures

REDUCE

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0 2) first(CATEGORIES) Є (N U T)

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Building a left-corner recognizer

Procedures

REDUCE

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0 2) first(CATEGORIES) Є (N U T) Input: SENTENCE with first = k1; CATEGORIES; CONSTITUENTS

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Building a left-corner recognizer

Procedures

REDUCE

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0 2) first(CATEGORIES) Є (N U T) Input: SENTENCE with first = k1; CATEGORIES; CONSTITUENTS Output: pop(SENTENCE); push(k2 ... kn t, CATEGORIES); push(k0, CONSTITUENTS)

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Building a left-corner recognizer

Procedures

REDUCE => delete first symbol from sentence ( = left corner of rule) => rest of right hand side of rule is pushed onto CATEGORIES together with signal symbol for end of rule 't' => CONSTITUENTS keeps in mind we are looking for k0

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Building a left-corner recognizer

Procedures

MOVE

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Building a left-corner recognizer

Procedures

MOVE

Preconditions:

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Building a left-corner recognizer

Procedures

MOVE

Preconditions: 1) first(CATEGORIES) = t

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Building a left-corner recognizer

Procedures

MOVE

Preconditions: 1) first(CATEGORIES) = t 2) first(CONSTITUENTS) = A Є (N U T)

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Building a left-corner recognizer

Procedures

MOVE

Preconditions: 1) first(CATEGORIES) = t 2) first(CONSTITUENTS) = A Є (N U T) Input: SENTENCE; CATEGORIES; CONSTITUENTS

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Building a left-corner recognizer

Procedures

MOVE

Preconditions: 1) first(CATEGORIES) = t 2) first(CONSTITUENTS) = A Є (N U T) Input: SENTENCE; CATEGORIES; CONSTITUENTS Output: push(first(CONSTITUENTS), SENTENCE); pop(CATEGORIES); pop(CONSTITUENTS)

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Building a left-corner recognizer

Procedures

MOVE => right-hand-side of rule whose left-hand-side is A has been completely processed, A was recognized => push A onto SENTENCE => remove the 't' from CATEGORIES => remove A from CONSTITUENTS

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Building a left-corner recognizer

Procedures

REMOVE

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Building a left-corner recognizer

Procedures

REMOVE

Precondition: first(SENTENCE) = first(CATEGORIES)

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Building a left-corner recognizer

Procedures

REMOVE

Precondition: first(SENTENCE) = first(CATEGORIES) Input: SENTENCE; CATEGORIES; CONSTITUENTS

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Building a left-corner recognizer

Procedures

REMOVE

Precondition: first(SENTENCE) = first(CATEGORIES) Input: SENTENCE; CATEGORIES; CONSTITUENTS Output: pop(SENTENCE); pop(CATEGORIES); CONSTITUENTS

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Building a left-corner recognizer

Procedures

REMOVE => is applied iff first(SENTENCE) is a category ki, a left corner, and this category has been recognized

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Building a left-corner recognizer

The Algorithm

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Building a left-corner recognizer

The Algorithm

RECOGNIZELC

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Building a left-corner recognizer

The Algorithm

RECOGNIZELC

Data: CFG G = <N, T, S, R> Lexicon L sentence w = w1 ... wn, n >= 1

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Building a left-corner recognizer

The Algorithm

RECOGNIZELC

Data: CFG G = <N, T, S, R> Lexicon L sentence w = w1 ... wn, n >= 1 Input: SENTENCE = [w1 ... wn]; CATEGORIES = [S]; CONSTITUENTS = [ ]

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Building a left-corner recognizer

The Algorithm

RECOGNIZELC

Data: CFG G = <N, T, S, R> Lexicon L sentence w = w1 ... wn, n >= 1 Input: SENTENCE = [w1 ... wn]; CATEGORIES = [S]; CONSTITUENTS = [ ] Output: true / false

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Building a left-corner recognizer

The Algorithm

RECOGNIZELC

Method: if (SENTENCE == CATEGORIES == CONSTITUENTS == [ ]) return true; else if (there is a procedure P Є {REDUCE, MOVE, REMOVE} whose preconditions are met) RECOGNIZELC(P(SENTENCE, CATEGORIES, CONSTITUENTS)); else return false;

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE [einen Fehler] [NP t VP t S] [VP S] REDUCE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE [einen Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [t NP t VP t S] [det VP S] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE [einen Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [t NP t VP t S] [det VP S] MOVE [det Fehler] [NP t VP t S] [VP S] REDUCE

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SLIDE 79

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE [einen Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [t NP t VP t S] [det VP S] MOVE [det Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [n t NP t VP t S] [NP VP S] REDUCE

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SLIDE 80

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [der Meister su...] [S] [ ] REDUCE [Meister sucht...] [t S] [det] MOVE [det Meister su...] [S] [ ] REDUCE [Meister sucht...] [n t S] [NP] REDUCE [sucht einen F...] [t n t S] [n NP] MOVE [n sucht einen F...] [n t S] [NP] REMOVE [sucht einen F...] [t S] [NP] MOVE [NP sucht einen...] [S] [ ] REDUCE [sucht einen F...] [VP t S] [S] REDUCE [einen Fehler] [t VP t S] [v S] MOVE [v einen Fehler] [VP t S] [S] REDUCE [einen Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [t NP t VP t S] [det VP S] MOVE [det Fehler] [NP t VP t S] [VP S] REDUCE [Fehler] [n t NP t VP t S] [NP VP S] REDUCE [ ] [t n t NP t VP t S] [n NP VP S] MOVE

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SLIDE 81

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE

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Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE

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SLIDE 83

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE

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SLIDE 84

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE

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SLIDE 85

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE [ ] [t VP t S] [VP S] MOVE

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SLIDE 86

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE [ ] [t VP t S] [VP S] MOVE [VP] [VP t S] [S] REMOVE

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SLIDE 87

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE [ ] [t VP t S] [VP S] MOVE [VP] [VP t S] [S] REMOVE [ ] [t S] [S] MOVE

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SLIDE 88

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE [ ] [t VP t S] [VP S] MOVE [VP] [VP t S] [S] REMOVE [ ] [t S] [S] MOVE [S] [S] [ ] REMOVE

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SLIDE 89

Building a left-corner recognizer

Example

Der Meister sucht einen Fehler SENTENCE CATEGORIES CONSTITUENTS procedure [ ] [t n t NP t VP t S] [n NP VP S] MOVE [n] [n t NP t VP t S] [NP VP S] REMOVE [ ] [t NP t VP t S] [NP VP S] MOVE [NP] [NP t VP t S] [VP S] REMOVE [ ] [t VP t S] [VP S] MOVE [VP] [VP t S] [S] REMOVE [ ] [t S] [S] MOVE [S] [S] [ ] REMOVE [ ] [ ] [ ] true

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SLIDE 90

Building a left-corner recognizer

Why is RECOGNIZELC non-deterministic?

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SLIDE 91

Building a left-corner recognizer

Why is RECOGNIZELC non-deterministic?

  • there may be several rules whose left corner is equal

to first(SENTENCE)

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SLIDE 92

Building a left-corner recognizer

Why is RECOGNIZELC non-deterministic?

  • there may be several rules whose left corner is equal

to first(SENTENCE)

  • there may be configurations where you could either

REDUCE or REMOVE:

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SLIDE 93

Building a left-corner recognizer

Why is RECOGNIZELC non-deterministic?

  • there may be several rules whose left corner is equal

to first(SENTENCE)

  • there may be configurations where you could either

REDUCE or REMOVE:

  • a newly created structure can be used to

complete the structure we are working at => REMOVE

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SLIDE 94

Building a left-corner recognizer

Why is RECOGNIZELC non-deterministic?

  • there may be several rules whose left corner is equal

to first(SENTENCE)

  • there may be configurations where you could either

REDUCE or REMOVE:

  • a newly created structure can be used to

complete the structure we are working at => REMOVE

  • or it could constitute a new structure of its own

=> REDUCE

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SLIDE 95

Building a left-corner recognizer

=> use breadth-first or depth-first search to check all possible configurations

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SLIDE 96

Building a left-corner recognizer

breadth-first search

RECOGNIZELC/BF

Data: CFG G = <N, T, S, R> Lexicon L sentence w = w1 ... wn, n >= 1 Input: SENTENCE = [w1 ... wn]; CATEGORIES = [S]; CONSTITUENTS = [ ] Output: true / false Structures: CONFIGS – set of configurations, null at the beginning

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SLIDE 97

Building a left-corner recognizer

breadth-first search

RECOGNIZELC/BF

Method: if (SENTENCE == CATEGORIES == CONSTITUENTS == [ ]) return true; else CONFIGS = set of all configurations derivable from the actual configuration using REMOVE, REDUCE or MOVE if (CONFIGS == null) return false; else for every configuration C Є CONFIGS: RECOGNIZELC/BF(SENTENCEC, CATEGORIESC, CONSTITUENTSC);

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SLIDE 98

Questions?

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SLIDE 99

A left-corner parsing algorithm

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SLIDE 100

A left-corner parsing algorithm

  • introduce another stack: STRUCTURE
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SLIDE 101

A left-corner parsing algorithm

  • introduce another stack: STRUCTURE
  • empty at the beginning; filled along the way
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SLIDE 102

A left-corner parsing algorithm

  • introduce another stack: STRUCTURE
  • empty at the beginning; filled along the way
  • return value: the structure stored in stack

STRUCTURE

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SLIDE 103

A left-corner parsing algorithm

Modifying the procedures

MOVELC/BF

Preconditions: 1) first(CATEGORIES) = t 2) first(CONSTITUENTS) = A Є (N U T) Input: SENTENCE; CATEGORIES; CONSTITUENTS; STRUCTURE Output: push(first(CONSTITUENTS), SENTENCE); pop(CATEGORIES); pop(CONSTITUENTS); STRUCTURE

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SLIDE 104

A left-corner parsing algorithm

Modifying the procedures

MOVELC/BF => just insert another parameter for the structure stack

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SLIDE 105

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0 2) first(CATEGORIES) Є (N U T) Input: SENTENCE with first = k1; CATEGORIES; CONSTITUENTS; STRUCTURE Output: pop(SENTENCE); push(k2 ... kn t, CATEGORIES); push(k0, CONSTITUENTS); structure1(k0, k1, STRUCTURE)

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SLIDE 106

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF – new subprocedure structure1

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SLIDE 107

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF – new subprocedure structure1 Input: STRUCTURE, symbols k0, k1 Є (N U T)

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SLIDE 108

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF – new subprocedure structure1 Input: STRUCTURE, symbols k0, k1 Є (N U T) Output: modified STRUCTURE'

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SLIDE 109

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF – new subprocedure structure1 Input: STRUCTURE, symbols k0, k1 Є (N U T) Output: modified STRUCTURE' Method: if (STRUCTURE == [ ] U first(STRUCTURE) == k'α with k' != k1)) return push((k0 k1), STRUCTURE) else return(push((k0 first(STRUCTURE)), pop(STRUCTURE)))

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SLIDE 110

A left-corner parsing algorithm

Modifying the procedures

REDUCELC/BF => add structure1(k0,k1,STRUCTURE) to output structure1: => if there is already a structure dominated by k1, integrate the new symbols, else build up a new structure description

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SLIDE 111

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF

Precondition: first(SENTENCE) = first(CATEGORIES) Input: SENTENCE; CATEGORIES; CONSTITUENTS; STRUCTURE Output: pop(SENTENCE); pop(CATEGORIES); CONSTITUENTS; structure2(CONSTITUENTS, STRUCTURE)

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SLIDE 112

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF – subprocedure structure2

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SLIDE 113

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF – subprocedure structure2 Input: CONSTITUENTS; STRUCTURE

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SLIDE 114

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF – subprocedure structure2 Input: CONSTITUENTS; STRUCTURE Output: modified STRUCTURE'

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SLIDE 115

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF – subprocedure structure2 Input: CONSTITUENTS; STRUCTURE Output: modified STRUCTURE' Method: if(CONSTITUENTS == [ ]) return STRUCTURE else return(push((second(STRUCTURE) + first(STRUCTURE)), pop(pop(STRUCTURE))))

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SLIDE 116

A left-corner parsing algorithm

Modifying the procedures

REMOVELC/BF with subprocedure structure2 => if CONSTITUENTS is not empty, associate the last two partial structure descriptions on STRUCTURE

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SLIDE 117

A left-corner parsing algorithm

Example

Eva sah Adam am Morgen SENTENCE CATEGORIES CONSTITUENTS STRUCTURE [Eva sah Adam...] [S] [ ] [ ] [sah Adam...] [t S] [n] [(n1)] [n sah Adam...] [S] [ ] [(n1)] [sah Adam...] [t S] [NP] [(NP(n1))] [NP sah Adam...] [S] [ ] [(NP(n1))] [sah Adam...] [VP t S] [S] [S(NP(n1))] [Adam am Morgen] [t VP t S] [v S] [(v2)(S(NP(n1)))] [v Adam am Morgen] [VP t S] [S] [(v2)(S(NP(n1)))] [Adam am Morgen] [NP PP t VP t S] [VP S] [(VP(v2))(S(NP...] [am Morgen] [t NP PP t VP t S] [n VP S] [(n3)(VP(v2))(S...] ... ... ... ...

(S (NP(n1)) (VP (v2) (NP(n3)) (PP (p4) (NP(n5)))))

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SLIDE 118

Questions?

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SLIDE 119

Left-corner parsing with look-ahead

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SLIDE 120

Left-corner parsing with look-ahead

  • become more efficient...
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SLIDE 121

Left-corner parsing with look-ahead

  • become more efficient...
  • ... by reducing number of rules that can be used

to generate next derivation

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SLIDE 122

Left-corner parsing with look-ahead

  • become more efficient...
  • ... by reducing number of rules that can be used

to generate next derivation

  • for every nonterminal n, calculate the set of all

symbols which are left corners of constituents reachable from n

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SLIDE 123

Left-corner parsing with look-ahead

  • become more efficient...
  • ... by reducing number of rules that can be used

to generate next derivation

  • for every nonterminal n, calculate the set of all

symbols which are left corners of constituents reachable from n => relation “LINK“

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SLIDE 124

Left-corner parsing with look-ahead

LINK(G)

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SLIDE 125

Left-corner parsing with look-ahead

LINK(G) set of all ordered pairs <X, Y> with X Є N and Y Є (N U T) which fulfill either of these conditions:

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SLIDE 126

Left-corner parsing with look-ahead

LINK(G) set of all ordered pairs <X, Y> with X Є N and Y Є (N U T) which fulfill either of these conditions:

1) X = Y (reflexivity)

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SLIDE 127

Left-corner parsing with look-ahead

LINK(G) set of all ordered pairs <X, Y> with X Є N and Y Є (N U T) which fulfill either of these conditions:

1) X = Y (reflexivity) 2) there is a rule X -> Yα Є R

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SLIDE 128

Left-corner parsing with look-ahead

LINK(G) set of all ordered pairs <X, Y> with X Є N and Y Є (N U T) which fulfill either of these conditions:

1) X = Y (reflexivity) 2) there is a rule X -> Yα Є R 3) <X, X'> Є LINK(G) and <X',Y> Є LINK(G) for an arbitrary X' Є N (transitivity)

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SLIDE 129

Left-corner parsing with look-ahead

LINK(G) set of all ordered pairs <X, Y> with X Є N and Y Є (N U T) which fulfill either of these conditions:

1) X = Y (reflexivity) 2) there is a rule X -> Yα Є R 3) <X, X'> Є LINK(G) and <X',Y> Є LINK(G) for an arbitrary X' Є N (transitivity)

=> should be calculated before parsing

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SLIDE 130

Left-corner parsing with look-ahead

Example

Grammar G with rules:

S -> X2 X3 X4 X2 -> e f X3 -> X1 X1 -> g X4 -> h

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SLIDE 131

Left-corner parsing with look-ahead

Example

Grammar G with rules:

S -> X2 X3 X4 X2 -> e f X3 -> X1 X1 -> g X4 -> h

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SLIDE 132

Left-corner parsing with look-ahead

Example

Grammar G with rules:

S -> X2 X3 X4 X2 -> e f X3 -> X1 X1 -> g X4 -> h LINK(G) = {<S,S>, <X1, X1>, <X2, X2>, <X3, X3>, <X4, X4>, <S, X2>, <S, e>, <X2, e>, <X1, g>, <X3, X1>, <X3, g>, <X4, h>

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SLIDE 133

Left-corner parsing with look-ahead

Example

Grammar G with rules:

S -> X2 X3 X4 X2 -> e f X3 -> X1 X1 -> g X4 -> h LINK(G) = {<S,S>, <X1, X1>, <X2, X2>, <X3, X3>, <X4, X4>, <S, X2>, <S, e>, <X2, e>, <X1, g>, <X3, X1>, <X3, g>, <X4, h> => strings like 'fghe' or 'hefg' needn't be parsed at all!

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SLIDE 134

Left-corner parsing with look-ahead

Modifying the procedures

  • nly necessary change: REDUCELC/LA

Preconditions: 1) There is a rule k0 -> k1 ... kn in R or k1 is part of k0 for an arbitrary lexical category k0 2) first(CATEGORIES) Є (N U T) 3) <first(CATEGORIES), k0> Є LINK(G) Input: SENTENCE with first = k1; CATEGORIES; CONSTITUENTS; STRUCTURE Output: pop(SENTENCE); push(k2 ... kn t, CATEGORIES); push(k0, CONSTITUENTS); structure1(STRUCTURE)

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SLIDE 135

Questions?

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SLIDE 136

Comparison to other approaches

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SLIDE 137

Comparison to other approaches

Drawback of top-down:

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SLIDE 138

Comparison to other approaches

Drawback of top-down:

  • ignores what the actual input string looks like most of

the time

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SLIDE 139

Comparison to other approaches

Drawback of top-down:

  • ignores what the actual input string looks like most of

the time

Drawback of bottom-up:

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SLIDE 140

Comparison to other approaches

Drawback of top-down:

  • ignores what the actual input string looks like most of

the time

Drawback of bottom-up:

  • we don't know what we're trying to build at the moment
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SLIDE 141

Comparison to other approaches

Drawback of top-down:

  • ignores what the actual input string looks like most of

the time

Drawback of bottom-up:

  • we don't know what we're trying to build at the moment

=> Left-corner can handle these... examples follow!

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SLIDE 142

Comparison to other approaches

Example TD vs LC

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SLIDE 143

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

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SLIDE 144

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died.

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SLIDE 145

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down:

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SLIDE 146

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP

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SLIDE 147

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP

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SLIDE 148

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

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SLIDE 149

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner:

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SLIDE 150

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD)

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SLIDE 151

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU)

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SLIDE 152

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

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SLIDE 153

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP'
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SLIDE 154

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
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SLIDE 155

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
  • > input: died – predict VP (TD)
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SLIDE 156

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
  • > input: died – predict VP (TD) -> recognize IV (BU)
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SLIDE 157

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
  • > input: died – predict VP (TD) -> recognize IV (BU)
  • > select rule 'VP -> IV'
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SLIDE 158

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
  • > input: died – predict VP (TD) -> recognize IV (BU)
  • > select rule 'VP -> IV' -> MATCH!
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SLIDE 159

Comparison to other approaches

Example TD vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV det -> the N -> robber PN -> Vincent IV -> died

Input sentence: Vincent died. Top-down: S -> NP VP -> det N VP -> DEAD END!

Vincent isn't det, det cannot be expanded => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize PN (BU) -> select rule 'NP -> PN'

  • > select rule 'S -> NP VP' -> MATCH!
  • > input: died – predict VP (TD) -> recognize IV (BU)
  • > select rule 'VP -> IV' -> MATCH! => successful parse
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SLIDE 160

Comparison to other approaches

Example BU vs LC

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SLIDE 161

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

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SLIDE 162

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died

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SLIDE 163

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up:

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SLIDE 164

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died

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SLIDE 165

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died

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SLIDE 166

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died

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SLIDE 167

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV

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SLIDE 168

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP

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SLIDE 169

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END!

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SLIDE 170

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

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SLIDE 171

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner:

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SLIDE 172

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD)

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SLIDE 173

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

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SLIDE 174

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N'
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SLIDE 175

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU)
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SLIDE 176

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
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SLIDE 177

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP'
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SLIDE 178

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP' -> input: died – predict VP (TD)
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SLIDE 179

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP' -> input: died – predict VP (TD) ->

recognize IV (BU)

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SLIDE 180

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP' -> input: died – predict VP (TD) ->

recognize IV (BU) -> select rule 'VP -> IV'

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SLIDE 181

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP '-> input: died – predict VP (TD) ->

recognize IV (BU) -> select rule 'VP -> IV'

  • > MATCH!
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SLIDE 182

Comparison to other approaches

Example BU vs LC

Grammar: S -> NP VP

NP -> det N NP -> PN VP -> IV VP -> TV NP TV -> plant IV -> died det -> the N -> plant

Input sentence: the plant died Bottom-up: the plant died -> det plant died -> det TV died -> det TV IV ->

det TV VP -> DEAD END! => need to backtrack ;-(

Left-corner: predict S (TD) -> recognize det (BU)

  • > select rule 'NP -> det N' -> recognize N (BU) -> MATCH!
  • > select rule 'S -> NP VP' -> input: died – predict VP (TD) ->

recognize IV (BU) -> select rule 'VP -> IV'

  • > MATCH! => successful parse
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SLIDE 183

Comparison to other approaches

Conclusion and outlook

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SLIDE 184

Comparison to other approaches

Conclusion and outlook

  • left-corner diminishes risk of having to

backtrack after a series of wrong moves

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SLIDE 185

Comparison to other approaches

Conclusion and outlook

  • left-corner diminishes risk of having to

backtrack after a series of wrong moves

  • but: also combines some of the problems TD

and BU have => hardly used in practice

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SLIDE 186

Comparison to other approaches

Conclusion and outlook

  • left-corner parsing might be a good model for

the human parser!

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SLIDE 187

Comparison to other approaches

Conclusion and outlook

  • left-corner parsing might be a good model for

the human parser!

Complexity issues:

Strategy Left-branching Center Embedding Right-branching TD O(n) O(n) O(1) BU O(1) O(n) O(n) LC O(1) O(n) O(1)

table taken from Shravan Vasishth's HSP slides

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SLIDE 188

Questions?

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SLIDE 189

Bibliography

  • Naumann, Sven and Langer, Haben 1994. Parsing.

Eine Einführung in die maschinelle Analyse natürlicher

  • Sprache. B.G. Teubner Stuttgart
  • a very short section from the Grune & Jacobs book
  • http://www.coli.uni-saarland.de/~kris/nlp-with-

prolog/html/node53.html

  • Shravan Vasishth's slides for the Human Sentence

Processing seminar from last semester

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SLIDE 190

Thanks for your attention!