On the Topological Complexity of omega-Languages of Non-Deterministic Petri Nets

Olivier Finkel (1, 2) , Michał Skrzypczak (3)

1 ELM - Équipe de Logique Mathématique
2 IMJ - Institut de Mathématiques de Jussieu
3 Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland.

We show that there are $\Sigma_3^0$-complete languages of infinite words accepted by non-deterministic Petri nets with Büchi acceptance condition, or equivalently by Büchi blind counter automata. This shows that omega-languages accepted by non-deterministic Petri nets are topologically more complex than those accepted by deterministic Petri nets.

Mots clés: complete sets; Languages of infinite words; Petri nets; Büchi acceptance condition; Cantor space; topological complexity; Borel hierarchy; complete sets.

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]

Olivier Finkel, Michał Skrzypczak. On the Topological Complexity of omega-Languages of Non-Deterministic Petri Nets. Information Processing Letters, 2014, 114 (5), pp.229-233. ⟨hal-00936744⟩