Sofic-Dyck shifts

Marie-Pierre Béal (1) , Michel Blockelet (2) , Catalin Dima (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LACL - Laboratoire d'Algorithmique Complexité et Logique

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck shifts are shifts of sequences whose finite factors form unambiguous context-free languages. We show that they correspond exactly to the class of shifts of sequences whose sets of factors are visibly pushdown languages. We give an expression of the zeta function of a sofic-Dyck shift.

Mots clés: Dyck shift; Markov-Dyck shift; sofic-Dyck shift; sofic shift; symbolic dynamics; visibly pushdown automaton; visibly pushdown language; zeta function

Domaines: Informatique et langage [cs.CL]

Marie-Pierre Béal, Michel Blockelet, Catalin Dima. Sofic-Dyck shifts. Theoretical Computer Science, 2016, 609, pp.226 - 244. ⟨10.1016/j.tcs.2015.09.027⟩. ⟨hal-01801266⟩