Geometrical regular languages and linear diophantine equations

Authors:
Jean-Marc Champarnaud;Jean-Philippe Dubernard;Franck Guingne;Hadrien Jeanne
Affiliations:
LITIS, Université de Rouen, France;LITIS, Université de Rouen, France;I3S, Université de Nice - Sophia Antipolis & CNRS, France;LITIS, Université de Rouen, France
Venue:
DCFS'11 Proceedings of the 13th international conference on Descriptional complexity of formal systems
Year:
2011

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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.