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Unique Decipherability in the Monoid of Languages: An Application of Rational Relations

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Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

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Abstract

We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages. We investigate a few subcases where the theory of rational relations can be employed to solve the problem. The case of unary languages is one of them and as a consequence, we show how to decide for two given finite subsets of nonnegative integers, whether they are the n-th root of a common set, for some n ≥ 1. We also show that it is decidable whether a finite collection of finite languages is a Parikh code, in the sense that whenever two products of these sets are commutatively equivalent, so are the sequences defining these products. Finally, we consider a nonunary special case where all finite sets consist of words containing exactly one occurrence of the specific letter.

This research was done during the second author’s visit at the LIAFA, CNRS UMR 7089, Université Paris Diderot, Novembre–December 2008. The second author was supported by the Academy of Finland under the grant 126211.

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Author information

Authors and Affiliations

  1. L.I.A.F.A., Université Paris 7, 2 Pl. Jussieu, 75 251, Paris Cedex, France

    Christian Choffrut

  2. Dept. of Math. and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

Authors
  1. Christian Choffrut
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  2. Juhani Karhumäki
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

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Choffrut, C., Karhumäki, J. (2009). Unique Decipherability in the Monoid of Languages: An Application of Rational Relations. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-03351-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03350-6

  • Online ISBN: 978-3-642-03351-3

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