Geometrical Regular Languages and Linear Diophantine Equations

  • Jean-Marc Champarnaud
  • Jean-Philippe Dubernard
  • Franck Guingne
  • Hadrien Jeanne
Conference paper

DOI: 10.1007/978-3-642-22600-7_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6808)
Cite this paper as:
Champarnaud JM., Dubernard JP., Guingne F., Jeanne H. (2011) Geometrical Regular Languages and Linear Diophantine Equations. In: Holzer M., Kutrib M., Pighizzini G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg

Abstract

We present a new method for checking whether a regular language over an arbitrarily large alphabet is semi-geometrical or whether it is geometrical. This method makes use first of the partitioning of the state diagram of the minimal automaton of the language into strongly connected components and secondly of the enumeration of the simple cycles in each component. It is based on the construction of systems of linear Diophantine equations the coefficients of which are deduced from the the set of simple cycles. This paper addresses the case of a strongly connected graph.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jean-Marc Champarnaud
    • 1
  • Jean-Philippe Dubernard
    • 1
  • Franck Guingne
    • 2
  • Hadrien Jeanne
    • 1
  1. 1.LITIS, Université de RouenFrance
  2. 2.I3S, Université de Nice - Sophia Antipolis & CNRSFrance

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