Recent results on syntactic groups of prefix codes

Jean Berstel (1) , Clelia de Felice (2) , Dominique Perrin (1) , Christophe Reutenauer (3) , Giuseppina Rindone (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 DIA - Dipartimento Informatica ed Applicazioni "Renato M. Capocelli"
3 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]

We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.

Domaines: Théorie et langage formel [cs.FL]

Jean Berstel, Clelia de Felice, Dominique Perrin, Christophe Reutenauer, Giuseppina Rindone. Recent results on syntactic groups of prefix codes. European Journal of Combinatorics, 2012, 33 (7), pp.1386-1401. ⟨hal-00790638⟩