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Emptiness of Zero Automata Is Decidable

Authors Mikolaj Bojanczyk, Hugo Gimbert, Edon Kelmendi

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Mikolaj Bojanczyk
Hugo Gimbert
Edon Kelmendi

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Mikolaj Bojanczyk, Hugo Gimbert, and Edon Kelmendi. Emptiness of Zero Automata Is Decidable. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 106:1-106:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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.
  • tree automata
  • probabilistic automata
  • monadic second-order logic


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