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Membership and Finiteness Problems for Rational Sets of Regular Languages

  • Sergey Afonin
  • Elena Hazova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)

Abstract

Let Σ be a finite alphabet. A set \(\mathcal{R}\) of regular languages over Σ is called rational if there exists a finite set \(\mathcal E\) of regular languages over Σ, such that \(\mathcal{R}\) is a rational subset of the finitely generated semigroup \((\mathcal{S},\cdot)=\langle\mathcal E\rangle\) with \(\mathcal E\) as the set of generators and language concatenation as a product. We prove that for any rational set \(\mathcal{R}\) and any regular language R ⊆ Σ* it is decidable (1) whether \(R\in\mathcal{R}\) or not, and (2) whether \(\mathcal{R}\) is finite or not.

Keywords

Regular Language Empty Word Short Word Free Semigroup Power Property 
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 2005

Authors and Affiliations

  • Sergey Afonin
    • 1
  • Elena Hazova
    • 1
  1. 1.Institute of MechanicsLomonosov Moscow State UniversityMoscowRussia

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