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. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Champarnaud, J. M., Dubernard, J. P., Guingne, F., & Jeanne, H. (2011). Geometrical regular languages and linear diophantine equations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6808 LNCS, pp. 107–120). https://doi.org/10.1007/978-3-642-22600-7_9
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