Document Open Access Logo

Good for Games Automata: From Nondeterminism to Alternation

Authors Udi Boker, Karoliina Lehtinen

PDF
Thumbnail PDF

File

LIPIcs.CONCUR.2019.19.pdf
  • Filesize: 0.52 MB
  • 16 pages

Document Identifiers

Author Details

Udi Boker
  • Interdisciplinary Center (IDC) Herzliya, Israel
Karoliina Lehtinen
  • University of Liverpool, United Kingdom

Funding

  • Boker, Udi: Israel Science Foundation grant 1373/16
  • Lehtinen, Karoliina: EPSRC grant EP/P020909/1 (Solving Parity Games in Theory and Practice)

Acknowledgements

We thank Orna Kupferman for suggesting to look into alternating good-for-games automata and for stimulating discussions on the subject, and Thomas Colcombet for introducing to us his work on alternating history-deterministic automata.

Cite AsGet BibTex

Udi Boker and Karoliina Lehtinen. Good for Games Automata: From Nondeterminism to Alternation. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CONCUR.2019.19

Abstract

A word automaton recognizing a language L is good for games (GFG) if its composition with any game with winning condition L preserves the game’s winner. While all deterministic automata are GFG, some nondeterministic automata are not. There are various other properties that are used in the literature for defining that a nondeterministic automaton is GFG, including "history-deterministic", "compliant with some letter game", "good for trees", and "good for composition with other automata". The equivalence of these properties has not been formally shown. We generalize all of these definitions to alternating automata and show their equivalence. We further show that alternating GFG automata are as expressive as deterministic automata with the same acceptance conditions and indices. We then show that alternating GFG automata over finite words, and weak automata over infinite words, are not more succinct than deterministic automata, and that determinizing Büchi and co-Büchi alternating GFG automata involves a 2^{Theta(n)} state blow-up. We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Good for games
  • history-determinism
  • alternation

Metrics

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

Related Versions

References

  1. Mikołaj Bojanczyk and Wojciech Czerwinski. An automata toolbox. Technical report, University of Warsaw, 2018. Google Scholar
  2. Udi Boker. Why These Automata Types? In Proceedings of LPAR, pages 143-163, 2018. Google Scholar
  3. Udi Boker, Denis Kuperberg, Orna Kupferman, and Michał Skrzypczak. Nondeterminism in the Presence of a Diverse or Unknown Future. In Proceedings of ICALP, pages 89-100, 2013. Google Scholar
  4. Udi Boker, Orna Kupferman, and Michał Skrzypczak. How Deterministic are Good-For-Games Automata? In Proceedings of FSTTCS, pages 18:1-18:14, 2017. Google Scholar
  5. Udi Boker, Orna Kupferman, and Adin Rosenberg. Alternation Removal in Büchi Automata. In Proceedings of ICALP, pages 76-87, 2010. Google Scholar
  6. Udi Boker and Karoliina Lehtinen. Register Games. Submitted to Logical Methods in Computer Science. Google Scholar
  7. Udi Boker and Karoliina Lehtinen. On the way to alternating weak automata. In Proceedings of FSTTCS, 2018. Google Scholar
  8. Udi Boker and Karoliina Lehtinen. Good for Games Automata: From Nondeterminism to Alternation. arXiv, 2019. URL: http://arxiv.org/abs/1906.11624.
  9. J 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
  10. Cristian S Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li, and Frank Stephan. Deciding parity games in quasipolynomial time. In Proceedings of STOC, pages 252-263, 2017. Google Scholar
  11. Thomas Colcombet. The theory of stabilisation monoids and regular cost functions. In Proceedings of ICALP, pages 139-150, 2009. Google Scholar
  12. Thomas Colcombet. Forms of Determinism for Automata. In Proceedings of STACS, pages 1-23, 2012. Google Scholar
  13. Thomas Colcombet. Fonctions régulières de coût. Habilitation à diriger les recherches, École Doctorale de Sciences Mathématiques de Paris Centre, 2013. Google Scholar
  14. Thomas Colcombet and Nathanaël Fijalkow. Universal graphs and Good for small games automata: New tools for infinite duration games. to appear in proc. of FOSSACS 2019. Google Scholar
  15. Wojciech Czerwiński, Laure Daviaud, Nathanaël Fijalkow, Marcin Jurdzińskit, Ranko Lazić, and Pawel Parys. Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games. In Proceedings of SODA, pages 2333-2349, 2019. Google Scholar
  16. Laure Daviaud, Marcin Jurdzinski, and Karoliina Lehtinen. Alternating Weak Automata from Universal Trees. Preprint arXiv, 2019. URL: http://arxiv.org/abs/1903.12620.
  17. Thomas Henzinger and Nir Piterman. Solving games without determinization. In Proceedings of CSL, pages 395-410, 2006. Google Scholar
  18. Denis Kuperberg and Michał Skrzypczak. On Determinisation of Good-For-Games Automata. In Proceedings of ICALP, pages 299-310, 2015. Google Scholar
  19. Orna Kupferman, Shmuel Safra, and Moshe Y Vardi. Relating word and tree automata. Ann. Pure Appl. Logic, 138(1-3):126-146, 2006. Conference version in 1996. Google Scholar
  20. Karoliina Lehtinen. A modal μ perspective on solving parity games in quasi-polynomial time. In Proceedings of LICS, pages 639-648, 2018. Google Scholar
  21. Satoru Miyano and Takeshi Hayashi. Alternating Finite Automata on ω-Words. Theoretical Computer Science, 32:321-330, 1984. Google Scholar
  22. Gila Morgenstern. Expressiveness results at the bottom of the ω-regular hierarchy. M.Sc. Thesis, The Hebrew University, 2003. 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