article

Inference of W-languages from prefixes

Authors:

C. de la Higuera,

J. C. JanodetAuthors Info & Claims

Theoretical Computer Science, Volume 313, Issue 2

Pages 295 - 312

https://doi.org/10.1016/j.tcs.2003.11.009

Published: 17 February 2004 Publication History

Abstract

Büchi automata are used to recognize languages of infinite strings. Such languages have been introduced to describe the behavior of real-time systems or infinite games. The question of inferring them from infinite examples has already been studied, but it may seem more reasonable to believe that the data from which we want to learn is a set of finite strings, namely the prefixes of accepted or rejected infinite strings. We describe the problems of identification in the limit and polynomial identification in the limit from given data associated to different interpretations of these prefixes: a positive prefix is universal (respectively existential) when all the infinite strings of which it is a prefix are in the language (respectively when at least one is); the same applies to the negative prefixes. We prove that the classes of regular ω-languages (those recognized by Büchi automata) and of deterministic ω-languages (those recognized by deterministic Büchi automata) are not identifiable in the limit, whatever interpretation for the prefixes is taken. We give a polynomial algorithm that identifies the class of safe languages from positive existential prefixes and negative universal prefixes. We show that this class is maximal for polynomial identification in the limit from given data, in the sense that no superclass can even be identified in the limit.

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Digital Library

Cited By

Ali SSun HZhao Y(2021)Model learning: a survey of foundations, tools and applicationsFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-019-9212-z15:5Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s11704-019-9212-z
Adriaans P(2006)Learning deterministic DEC grammars is learning rational numbersProceedings of the 8th international conference on Grammatical Inference: algorithms and applications10.1007/11872436_26(320-326)Online publication date: 20-Sep-2006
https://dl.acm.org/doi/10.1007/11872436_26

Index Terms

Inference of W-languages from prefixes
1. Computing methodologies
  1. Artificial intelligence
    1. Natural language processing
  2. Machine learning
    1. Learning paradigms
2. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages
  2. Models of computation
    1. Computability

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Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 313, Issue 2

Special issue: Algorithmic learning theory

17 February 2004

138 pages

ISSN:0304-3975

Issue’s Table of Contents

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 17 February 2004

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Cited By

Ali SSun HZhao Y(2021)Model learning: a survey of foundations, tools and applicationsFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-019-9212-z15:5Online publication date: 1-Oct-2021
https://dl.acm.org/doi/10.1007/s11704-019-9212-z
Adriaans P(2006)Learning deterministic DEC grammars is learning rational numbersProceedings of the 8th international conference on Grammatical Inference: algorithms and applications10.1007/11872436_26(320-326)Online publication date: 20-Sep-2006
https://dl.acm.org/doi/10.1007/11872436_26

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