Document Open Access Logo

On Guidable Index of Tree Automata

Authors Damian Niwiński , Michał Skrzypczak

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2021.81.pdf
  • Filesize: 0.68 MB
  • 14 pages

Document Identifiers

Author Details

Damian Niwiński
  • Institute of Informatics, University of Warsaw, Poland
Michał Skrzypczak
  • Institute of Informatics, University of Warsaw, Poland

Funding

  • Skrzypczak, Michał: Supported by the Polish NCN grant 2016/22/E/ST6/00041.

Cite AsGet BibTex

Damian Niwiński and Michał Skrzypczak. On Guidable Index of Tree Automata. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 81:1-81:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.81

Abstract

We study guidable parity automata over infinite trees introduced by Colcombet and Löding, which form an expressively complete subclass of all non-deterministic tree automata. We show that, for any non-deterministic automaton, an equivalent guidable automaton with the smallest possible index can be effectively found. Moreover, if an input automaton is of a special kind, i.e. it is deterministic or game automaton then a guidable automaton with an optimal index can be deterministic (respectively game) automaton as well. Recall that the problem whether an equivalent non-deterministic automaton with the smallest possible index can be effectively found is open, and a positive answer is known only in the case when an input automaton is a deterministic, or more generally, a game automaton.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • guidable automata
  • index problem
  • ω-regular games

Metrics

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

References

  1. Julian Bradfield. Simplifying the modal mu-calculus alternation hierarchy. In STACS, pages 39-49, 1998. Google Scholar
  2. Julius Richard Büchi. On a decision method in restricted second-order arithmetic. In Proc. 1960 Int. Congr. for Logic, Methodology and Philosophy of Science, pages 1-11, 1962. Google Scholar
  3. Julius Richard Büchi and Lawrence H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295-311, 1969. Google Scholar
  4. Cristian S. Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li, and Frank Stephan. Deciding parity games in quasipolynomial time. In 49th Annual ACM STOC, pages 252-263, 2017. Google Scholar
  5. Lorenzo Clemente and Michał Skrzypczak. Deterministic and game separability for regular languages of infinite trees. accepted to ICALP, 2021. Google Scholar
  6. Lorenzo Clemente and Michał Skrzypczak. Deterministic and game separability for regular languages of infinite trees, 2021. URL: http://arxiv.org/abs/2105.01137.
  7. Thomas Colcombet and Christof Löding. The non-deterministic Mostowski hierarchy and distance-parity automata. In ICALP (2), pages 398-409, 2008. Google Scholar
  8. Jacques Duparc, Alessandro Facchini, and Filip Murlak. Linear game automata: Decidable hierarchy problems for stripped-down alternating tree automata. In CSL, pages 225-239, 2009. Google Scholar
  9. E. Allen Emerson and Charanjit S. Jutla. The complexity of tree automata and logics of programs (extended abstract). In 29th FOCS, pages 328-337, 1988. Google Scholar
  10. E. Allen Emerson and Charanjit S. Jutla. Tree automata, mu-calculus and determinacy. In FOCS, pages 368-377, 1991. Google Scholar
  11. Alessandro Facchini, Filip Murlak, and Michał Skrzypczak. Index problems for game automata. ACM Transactions on Computational Logic, 17(4):24:1-24:38, 2016. Google Scholar
  12. Erich Grädel, Wolfgang Thomas, and Thomas Wilke, editors. Automata, Logics, and Infinite Games: A Guide to Current Research, volume 2500 of Lecture Notes in Computer Science. Springer, 2002. Google Scholar
  13. Yuri Gurevich and Leo Harrington. Trees, automata, and games. In STOC, pages 60-65, 1982. Google Scholar
  14. Christof Löding. Logic and automata over infinite trees. Habilitation thesis, RWTH Aachen University, 2009. Google Scholar
  15. Andrzej W. Mostowski. Regular expressions for infinite trees and a standard form of automata. In Symposium on Computation Theory, pages 157-168, 1984. Google Scholar
  16. Damian Niwiński. On fixed-point clones. In ICALP, pages 464-473, 1986. Google Scholar
  17. Damian Niwiński. Fixed point characterization of infinite behavior of finite-state systems. Theoretical Computer Science, 189(1-2):1-69, 1997. Google Scholar
  18. Damian Niwiński and Igor Walukiewicz. Deciding nondeterministic hierarchy of deterministic tree automata. Electronic Notes on Theoretical Computer Science, 123:195-208, 2005. Google Scholar
  19. Michael Oser Rabin. Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society, 141:1-35, 1969. Google Scholar
  20. Michael Oser Rabin. Weakly definable relations and special automata. In Proceedings of the Symposium on Mathematical Logic and Foundations of Set Theory, pages 1-23. North-Holland, 1970. Google Scholar
  21. Wolfgang Thomas. Languages, automata, and logic. In Handbook of Formal Languages, pages 389-455. Springer, 1996. Google Scholar
  22. Klaus Wagner. On ω-regular sets. Information and Control, 43(2):123-177, 1979. 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
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact