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

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:
Theoretical Computer Science
Year:
2012

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Abstract

Given an arbitrarily large alphabet @S, we consider the family of regular languages over @S 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.