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Geometrical regular languages and linear Diophantine equations: The strongly connected case

Abstract : Given an arbitrarily large alphabet Σ, we consider the family of regular languages over Σ for which the deterministic minimal automaton has a strongly connected state diagram. We present a new method for checking whether such a language is semi-geometrical or not and whether it is geometrical or not. This method makes use of the enumeration of the simple cycles of the state diagram. It is based on the construction of systems of linear Diophantine equations, where the coefficients are deduced from the set of simple cycles
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https://hal.archives-ouvertes.fr/hal-00906811
Contributor : Jean-Philippe Dubernard <>
Submitted on : Wednesday, November 20, 2013 - 1:16:13 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:34 PM

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  • HAL Id : hal-00906811, version 1

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Jean-Marc Champarnaud, Jean-Philippe Dubernard, Franck Guingne, Hadrien Jeanne. Geometrical regular languages and linear Diophantine equations: The strongly connected case. Theoretical Computer Science, Elsevier, 2012, 449, pp.54-63. ⟨hal-00906811⟩

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