Languages recognized by finite supersoluble groups

Olivier Carton (1) , Jean-Eric Pin (1) , Xaro Soler-Escrivà (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Dpt. de Matemàtica Aplicada

In this paper, we give two descriptions of the languages recognized by finite supersoluble groups. We first show that such a language belongs to the Boolean algebra generated by the modular products of elementary commutative languages. An elementary commutative language is defined by a condition specifying the number of occurrences of each letter in its words, modulo some fixed integer. Our second characterization makes use of counting functions computed by transducers in strict triangular form.

Mots clés: Finite Automata; Supersoluble group; transducer; variety of languages

Domaines: Autre [cs.OH]; Mathématique discrète [cs.DM]

Olivier Carton, Jean-Eric Pin, Xaro Soler-Escrivà. Languages recognized by finite supersoluble groups. 2007. ⟨hal-00143945⟩