Emptiness of zero automata is decidable

Mikołaj Bojańczyk (1) , Hugo Gimbert (2) , Edon Kelmendi (2)

1 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Zero automata are a probabilistic extension of parity automata on infinite trees. The satisfiability of a certain probabilistic variant of mso, called tmso + zero, reduces to the emptiness problem for zero automata. We introduce a variant of zero automata called nonzero automata. We prove that for every zero automaton there is an equivalent nonzero automaton of quadratic size and the emptiness problem of nonzero automata is decidable and both in NP and in coNP. These results imply that tmso + zero has decidable satisfiability.

Mots clés: monadic second-order logic; probabilistic automata; tree automata

Domaines: Théorie et langage formel [cs.FL]; Informatique et théorie des jeux [cs.GT]

Mikołaj Bojańczyk, Hugo Gimbert, Edon Kelmendi. Emptiness of zero automata is decidable. 2017. ⟨hal-01470940v2⟩