Alternating Nonzero Automata

Authors Paulin Fournier, Hugo Gimbert

Thumbnail PDF


  • Filesize: 0.53 MB
  • 16 pages

Document Identifiers

Author Details

Paulin Fournier
  • LS2N, Université de Nantes, France
Hugo Gimbert
  • CNRS, LaBRI, Université de Bordeaux, France

Cite AsGet BibTex

Paulin Fournier and Hugo Gimbert. Alternating Nonzero Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 13:1-13:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We introduce a new class of automata on infinite trees called alternating nonzero automata, which extends the class of non-deterministic nonzero automata. The emptiness problem for this class is still open, however we identify a subclass, namely limited choice, for which we reduce the emptiness problem for alternating nonzero automata to the same problem for non-deterministic ones, which implies decidability. We obtain, as corollaries, algorithms for the satisfiability of a probabilistic temporal logic extending both CTL* and the qualitative fragment of pCTL*.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • zero-automata
  • probabilities
  • temporal logics


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Christel Baier, Marcus Größer, and Nathalie Bertrand. Probabilistic ω-automata. J. ACM, 59(1):1, 2012. Google Scholar
  2. Mikołaj Bojańczyk. Thin MSO with a probabilistic path quantifier. In 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, pages 96:1-96:13, 2016. Google Scholar
  3. Mikołaj Bojańczyk, Hugo Gimbert, and Edon Kelmendi. Emptiness of zero automata is decidable. CoRR, abs/1702.06858, 2017. URL:
  4. Mikołaj Bojańczyk, Hugo Gimbert, and Edon Kelmendi. Emptiness of zero automata is decidable. In 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, pages 106:1-106:13, 2017. Google Scholar
  5. Tomás; Brázdil, Vojtech Forejt, Jan Kretínský, and Antonín Kucera. The satisfiability problem for probabilistic CTL. In Proc. of LICS, pages 391-402, 2008. Google Scholar
  6. Tomáš Brázdil, Vojtěch Forejt, and Antonín Kučera. Controller synthesis and verification for markov decision processes with qualitative branching time objectives. Automata, Languages and Programming, pages 148-159, 2008. Google Scholar
  7. Arnaud Carayol, Axel Haddad, and Olivier Serre. Randomization in automata on infinite trees. ACM Trans. Comput. Log., 15(3):24:1-24:33, 2014. Google Scholar
  8. Ashok K. Chandra, Dexter C. Kozen, and Larry J. Stockmeyer. Alternation. J. ACM, 28(1):114-133, January 1981. Google Scholar
  9. E Allen Emerson and Joseph Y Halpern. Sometimes and not never revisited: on branching versus linear time temporal logic. Journal of the ACM (JACM), 33(1):151-178, 1986. Google Scholar
  10. Yuri Gurevich and Leo Harrington. Trees, automata, and games. In Proceedings of STOC'82, pages 60-65, New York, NY, USA, 1982. ACM. Google Scholar
  11. Hans Hansson and Bengt Jonsson. A logic for reasoning about time and reliability. Formal aspects of computing, 6(5):512-535, 1994. Google Scholar
  12. Orna Kupferman, Moshe Y Vardi, and Pierre Wolper. An automata-theoretic approach to branching-time model checking. Journal of the ACM (JACM), 47(2):312-360, 2000. Google Scholar
  13. Daniel Lehmann and Saharon Shelah. Reasoning with time and chance. Information and Control, 53(3):165-1983, 1982. Google Scholar
  14. Henryk Michalewski and Matteo Mio. Measure quantifier in monadic second order logic. In Proc. of LFCS 2016, pages 267-282, 2016. URL:
  15. Henryk Michalewski, Matteo Mio, and Mikołaj Bojańczyk. On the regular emptiness problem of subzero automata. In Proc. of ICE 2016, Heraklion, Greece, 8-9 June 2016., pages 1-23, 2016. Google Scholar
  16. David E. Muller and Paul E. Schupp. Alternating automata on infinite trees. Theoretical Computer Science, 54(2):267 - 276, 1987. URL:
  17. A. Paz. Introduction to probabilistic automata. Academic Press, 1971. Google Scholar
  18. M. O. Rabin. Probabilistic automata. Information and Control, 6(3):230-245, 1963. Google Scholar
  19. Moshe Y Vardi and Larry Stockmeyer. Improved upper and lower bounds for modal logics of programs. In Proceedings of the seventeenth annual ACM symposium on Theory of computing, pages 240-251. ACM, 1985. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail