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Geometrical Regular Languages and Linear Diophantine Equations

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Descriptional Complexity of Formal Systems (DCFS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6808))

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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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Author information

Authors and Affiliations

  1. LITIS, Université de Rouen, France

    Jean-Marc Champarnaud, Jean-Philippe Dubernard & Hadrien Jeanne

  2. I3S, Université de Nice - Sophia Antipolis & CNRS, France

    Franck Guingne

Authors
  1. Jean-Marc Champarnaud
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  2. Jean-Philippe Dubernard
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  3. Franck Guingne
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  4. Hadrien Jeanne
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Markus Holzer

  2. Institut für Informatik, Universität Gießen, Arndtstraße 2, 35392, Gießen, Germany

    Martin Kutrib

  3. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy

    Giovanni Pighizzini

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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. https://doi.org/10.1007/978-3-642-22600-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-22600-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22599-4

  • Online ISBN: 978-3-642-22600-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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