Mind Change Complexity of Inferring Unbounded Unions of Pattern Languages from Positive Data

  • Matthew de Brecht
  • Akihiro Yamamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4264)

Abstract

This paper gives a proof that the class of unbounded unions of languages of regular patterns with constant segment length bound is inferable from positive data with mind change bound between ωω and \(\omega^{\omega^{\omega}}\). We give a very tight bound on the mind change complexity based on the length of the constant segments and the size of the alphabet of the pattern languages. This is, to the authors’ knowledge, the first time a natural class of languages has been shown to be inferable with mind change complexity above ωω. The proof uses the notion of closure operators on a class of languages, and also uses the order type of well-partial-orderings to obtain a mind change bound. The inference algorithm presented can be easily applied to a wide range of classes of languages. Finally, we show an interesting connection between proof theory and mind change complexity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthew de Brecht
    • 1
  • Akihiro Yamamoto
    • 1
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan

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