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Typed pattern languages and their learnability

  • Takeshi Koshiba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)

Abstract

In this paper, we extend patterns, introduced by Angluin [Ang80b], to typed patterns by introducing types into variables. A type is a recursive language and a variable of the type is substituted only with an element in the recursive language. This extension enhances the expressive power of patterns with preserving their good properties. First, we give a general learnability result for typed pattern languages. We show that if a class of types has finite elasticity then the typed pattern language is identifiable in the limit from positive data. Next, we give a useful tool to show the conservative learnability of typed pattern languages. That is, if an indexed family \({\cal L}\)of recursive languages has recursive finite thickness and the equivalence problem for \({\cal L}\) is decidable, then \({\cal L}\) is conservatively learnable from positive data. Using this tool, we consider the following classes of types: (1) the class of all strings over subsets of the alphabet, (2) the class of all untyped pattern languages, and (3) a class of k-bounded regular languages. We show that each of these typed pattern languages is conservatively learnable from positive data.

Keywords

Infinite Sequence Equivalence Problem Regular Language Positive Data Pattern Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Takeshi Koshiba
    • 1
  1. 1.Institute for Social Information ScienceFujitsu Laboratories Ltd.ShizuokaJapan

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