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LING 406 Intro to Computational Linguistics Complexity of Natural Language

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There have been many arguments about the complexity of natural language, but all ... This hinges crucially on the competence-performance distinction. ... – PowerPoint PPT presentation

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Title: LING 406 Intro to Computational Linguistics Complexity of Natural Language


1
LING 406Intro to Computational
LinguisticsComplexity of Natural Language
  • Richard Sproat
  • URL http//catarina.ai.uiuc.edu/L406_08/

2
This Lecture
  • Chomsky hierarchy
  • Computational complexity of natural language

3
Chomsky hierarchy
4
Chomsky hierarchy
  • Note that there is strict containment here e.g.,
    all regular languages are context free languages
    all context free languages are context-sensitive
    languages etc.
  • Question Where do human languages fall on this
    hierarchy?

5
Complexity of natural language
  • There have been many arguments about the
    complexity of natural language, but all of them
    have the following form
  • Find a particular construction type C (e.g.
    center embedding) in a natural language L (e.g.
    English)
  • Assume that the construction type in question is
    theoretically unbounded i.e., in theory speakers
    could go on producing ever longer instances of
    the construction.
  • The fact that in real life there is a limit to
    the length of instances of C that people can
    process is held to be irrelevant.
  • This hinges crucially on the competence-performanc
    e distinction.
  • Reduce C via a homomorphism to a formal
    expression of known complexity.
  • Argue thereby that L cannot be of lesser
    complexity than C.
  • Extrapolate from this one instance to natural
    language in general. I.e. if theres this one
    construction in this one language that has this
    complexity then the human language faculty must
    allow this in general.
  • Caveat in order for this argument to be correct
    it is not sufficient in general to show that L
    contains C to draw conclusions about L from C.

6
NL is not regular Chomskys original argument
7
Why Chomskys argument is fallacious
8
How to state the observation correctly
9
Similar point about center-embedding
10
Center embedding
English
ab
anbn
11
Can we go higher on the hierarchy?
  • In morphology reduplication in Bambara (Culy,
    1985), which weve seen a couple of times.
  • In syntax cross-serial dependencies in Swiss
    German (Shieber, 1985)

12
Swiss German
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