Document Open Access Logo

Degrees of Ambiguity for Parity Tree Automata

Authors Alexander Rabinovich , Doron Tiferet

PDF
Thumbnail PDF

File

LIPIcs.CSL.2021.36.pdf
  • Filesize: 0.55 MB
  • 20 pages

Document Identifiers

Author Details

Alexander Rabinovich
  • Tel Aviv University, Israel
Doron Tiferet
  • Tel Aviv University, Israel

Funding

Supported in part by Len Blavatnik and the Blavatnik Family foundation.

Acknowledgements

We would like to thank the reviewers for their useful suggestions. The first author is grateful to Michał Skrzypczak for very fruitful discussions.

Cite AsGet BibTex

Alexander Rabinovich and Doron Tiferet. Degrees of Ambiguity for Parity Tree Automata. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 36:1-36:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CSL.2021.36

Abstract

An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is k ∈ ℕ, such that for every input it has at most k accepting computations. We consider Parity Tree Automata (PTA) and prove that the problem whether a PTA is not unambiguous (respectively, is not boundedly ambiguous, not finitely ambiguous) is co-NP complete, and the problem whether a PTA is not countably ambiguous is co-NP hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • automata on infinite trees
  • degree of ambiguity
  • omega word automata
  • parity automata

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Vince Bárány, Łukasz Kaiser, and Alex Rabinovich. Expressing cardinality quantifiers in monadic second-order logic over trees. Fundamenta Informaticae, 100(1-4):1-17, 2010. Google Scholar
  2. Krishnendu Chatterjee, Thomas A Henzinger, and Nir Piterman. Generalized parity games. In International Conference on Foundations of Software Science and Computational Structures, pages 153-167. Springer, 2007. Google Scholar
  3. Thomas Colcombet. Unambiguity in automata theory. In International Workshop on Descriptional Complexity of Formal Systems, pages 3-18. Springer, 2015. Google Scholar
  4. Yo-Sub Han, Arto Salomaa, and Kai Salomaa. Ambiguity, nondeterminism and state complexity of finite automata. Acta Cybernetica, 23(1):141-157, 2017. Google Scholar
  5. Jozef Jirásek, Galina Jirásková, and Juraj Šebej. Operations on unambiguous finite automata. In International Conference on Developments in Language Theory, pages 243-255. Springer, 2016. Google Scholar
  6. Ernst Leiss. Succinct representation of regular languages by boolean automata. Theoretical computer science, 13(3):323-330, 1981. Google Scholar
  7. Hing Leung. Descriptional complexity of nfa of different ambiguity. International Journal of Foundations of Computer Science, 16(05):975-984, 2005. Google Scholar
  8. Christof Löding and Anton Pirogov. On finitely ambiguous büchi automata. In Mizuho Hoshi and Shinnosuke Seki, editors, Developments in Language Theory - 22nd International Conference, DLT 2018, Tokyo, Japan, September 10-14, 2018, Proceedings, volume 11088 of Lecture Notes in Computer Science, pages 503-515. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-98654-8_41.
  9. Dominique Perrin and Jean-Éric Pin. Infinite words: automata, semigroups, logic and games, volume 141. Academic Press, 2004. Google Scholar
  10. Alexander Rabinovich. Complementation of finitely ambiguous Büchi automata. In International Conference on Developments in Language Theory, pages 541-552. Springer, 2018. Google Scholar
  11. Alexander Rabinovich and Doron Tiferet. Degrees of ambiguity of büchi tree automata. In Arkadev Chattopadhyay and Paul Gastin, editors, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2019, December 11-13, 2019, Bombay, India, volume 150 of LIPIcs, pages 50:1-50:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2019.50.
  12. Helmut Seidl. On the finite degree of ambiguity of finite tree automata. Acta Informatica, 26(6):527-542, 1989. Google Scholar
  13. Richard Edwin Stearns and Harry B Hunt III. On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata. SIAM Journal on Computing, 14(3):598-611, 1985. Google Scholar
  14. Wolfgang Thomas. Automata on infinite objects. In Formal Models and Semantics, pages 133-191. Elsevier, 1990. Google Scholar
  15. Andreas Weber and Helmut Seidl. On the degree of ambiguity of finite automata. Theoretical Computer Science, 88(2):325-349, 1991. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023 Schloss Dagstuhl - LZI GmbH Imprint Privacy Contact