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)


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.


Regular Language Empty Word Short Word Free Semigroup Power Property 
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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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