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Learning Unions of k-Testable Languages

  • Alexis LinardEmail author
  • Colin de la Higuera
  • Frits Vaandrager
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)

Abstract

A classical problem in grammatical inference is to identify a language from a set of examples. In this paper, we address the problem of identifying a union of languages from examples that belong to several different unknown languages. Indeed, decomposing a language into smaller pieces that are easier to represent should make learning easier than aiming for a too generalized language. In particular, we consider k-testable languages in the strict sense (k-TSS). These are defined by a set of allowed prefixes, infixes (sub-strings) and suffixes that words in the language may contain. We establish a Galois connection between the lattice of all languages over alphabet \(\varSigma \), and the lattice of k-TSS languages over \(\varSigma \). We also define a simple metric on k-TSS languages. The Galois connection and the metric allow us to derive an efficient algorithm to learn the union of k-TSS languages. We evaluate our algorithm on an industrial dataset and thus demonstrate the relevance of our approach.

Keywords

Grammatical inference k-Testable languages Union of languages Galois connection 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexis Linard
    • 1
    Email author
  • Colin de la Higuera
    • 2
  • Frits Vaandrager
    • 1
  1. 1.Institute for Computing and Information ScienceRadboud UniversityNijmegenThe Netherlands
  2. 2.Laboratoire des Sciences du Numérique de NantesUniversité de NantesNantesFrance

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