Emptiness of Zero Automata Is Decidable


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, with complexity co-np. These results imply that tmso + zero has decidable satisfiability.

In 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland