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The Complexity of Rational Synthesis

Authors Rodica Condurache, Emmanuel Filiot, Raffaella Gentilini, Jean-François Raskin



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Rodica Condurache
Emmanuel Filiot
Raffaella Gentilini
Jean-François Raskin

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Rodica Condurache, Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The Complexity of Rational Synthesis. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 121:1-121:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ICALP.2016.121

Abstract

We study the computational complexity of the cooperative and non-cooperative rational synthesis problems, as introduced by Kupferman, Vardi and co-authors. We provide tight results for most of the classical omega-regular objectives, and show how to solve those problems optimally.
Keywords
  • Non-zero sum games
  • reactive synthesis
  • omega-regular objectives

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References

  1. Benjamin Aminof and Sasha Rubin. First cycle games. In Proceedings 2nd International Workshop on Strategic Reasoning, SR 2014, Grenoble, France, April 5-6, 2014., pages 83-90, 2014. URL: http://dx.doi.org/10.4204/EPTCS.146.11.
  2. Christel Baier and Joost-Pieter Katoen. Principles of model checking. MIT Press, 2008. Google Scholar
  3. Dietmar Berwanger. Admissibility in infinite games. In STACS 2007, 24th Annual Symposium on Theoretical Aspects of Computer Science, Aachen, Germany, February 22-24, 2007, Proceedings, volume 4393 of Lecture Notes in Computer Science, pages 188-199. Springer, 2007. Google Scholar
  4. Romain Brenguier, Lorenzo Clemente, Paul Hunter, Guillermo A. Pérez, Mickael Randour, Jean-François Raskin, Ocan Sankur, and Mathieu Sassolas. Non-zero sum games for reactive synthesis. CoRR, abs/1512.05568, 2015. URL: http://arxiv.org/abs/1512.05568.
  5. Romain Brenguier, Jean-François Raskin, and Ocan Sankur. Assume-admissible synthesis. In 26th International Conference on Concurrency Theory, CONCUR 2015, Madrid, Spain, September 1.4, 2015, volume 42 of LIPIcs, pages 100-113. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2015. URL: http://dx.doi.org/10.4230/LIPIcs.CONCUR.2015.100.
  6. Romain Brenguier, Jean-François Raskin, and Mathieu Sassolas. The complexity of admissibility in omega-regular games. In Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS'14, Vienna, Austria, July 14-18, 2014, pages 23:1-23:10. ACM, 2014. Google Scholar
  7. Krishnendu Chatterjee, Laurent Doyen, Emmanuel Filiot, and Jean-François Raskin. Doomsday equilibria for omega-regular games. In Verification, Model Checking, and Abstract Interpretation - 15th International Conference, VMCAI 2014, San Diego, CA, USA, January 19-21, 2014, Proceedings, volume 8318 of Lecture Notes in Computer Science, pages 78-97. Springer, 2014. Google Scholar
  8. Krishnendu Chatterjee and Thomas A. Henzinger. Assume-guarantee synthesis. In Tools and Algorithms for the Construction and Analysis of Systems, 13th International Conference, TACAS 2007, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2007 Braga, Portugal, March 24 - April 1, 2007, Proceedings, volume 4424 of Lecture Notes in Computer Science, pages 261-275. Springer, 2007. Google Scholar
  9. Krishnendu Chatterjee, Thomas A. Henzinger, and Marcin Jurdzinski. Games with secure equilibria. Theor. Comput. Sci., 365(1-2):67-82, 2006. URL: http://dx.doi.org/10.1016/j.tcs.2006.07.032.
  10. Krishnendu Chatterjee, Thomas A. Henzinger, and Nir Piterman. Generalized parity games. In Proceedings of the 10th International Conference on Foundations of Software Science and Computational Structures, FOSSACS'07, pages 153-167, Berlin, Heidelberg, 2007. Springer-Verlag. URL: http://dl.acm.org/citation.cfm?id=1760037.1760051.
  11. Alessandro Cimatti, Edmund M. Clarke, Enrico Giunchiglia, Fausto Giunchiglia, Marco Pistore, Marco Roveri, Roberto Sebastiani, and Armando Tacchella. Nusmv 2: An opensource tool for symbolic model checking. In Computer Aided Verification, 14th International Conference, CAV 2002,Copenhagen, Denmark, July 27-31, 2002, Proceedings, volume 2404 of Lecture Notes in Computer Science, pages 359-364. Springer, 2002. Google Scholar
  12. Rodica Condurache, Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The complexity of rational synthesis - full version. Available at: http://lacl.fr/˜rbozianu/papers/fullRationalSynthesis.pdf, 2016.
  13. Marco Faella. Admissible strategies in infinite games over graphs. In Mathematical Foundations of Computer Science 2009, 34th International Symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009. Proceedings, volume 5734 of Lecture Notes in Computer Science, pages 307-318. Springer, 2009. Google Scholar
  14. Dana Fisman, Orna Kupferman, and Yoad Lustig. Rational synthesis. CoRR, abs/0907.3019, 2009. URL: http://arxiv.org/abs/0907.3019.
  15. Yuri Gurevich and Leo Harrington. Trees, automata, and games. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, STOC'82, pages 60-65, New York, NY, USA, 1982. ACM. URL: http://dx.doi.org/10.1145/800070.802177.
  16. Paul Hunter and Anuj Dawar. Complexity bounds for regular games. In Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science (MFCS), Lecture Notes in Computer Science, pages 495-506, Berlin, Heidelberg, 2005. Springer-Verlag. Google Scholar
  17. M. Jurdzinski. Algorithms for solving parity games. In Lectures in Game Theory for Computer Scientists, pages 74-98. Cambridge University Press, 2011. Google Scholar
  18. Marcin Jurdzinski, Mike Paterson, and Uri Zwick. A deterministic subexponential algorithm for solving parity games. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2006, Miami, Florida, USA, January 22-26, 2006, pages 117-123, 2006. URL: http://dl.acm.org/citation.cfm?id=1109557.1109571.
  19. Orna Kupferman, Giuseppe Perelli, and Moshe Y. Vardi. Synthesis with rational environments. In Multi-Agent Systems - 12th European Conference, EUMAS 2014, Prague, Czech Republic, December 18-19, 2014, Revised Selected Papers, pages 219-235, 2014. URL: http://dx.doi.org/10.1007/978-3-319-17130-2_15.
  20. Fabio Mogavero, Aniello Murano, Giuseppe Perelli, and Moshe Y. Vardi. What makes atl* decidable? A decidable fragment of strategy logic. In CONCUR 2012 - Concurrency Theory - 23rd International Conference, CONCUR 2012, Newcastle upon Tyne, UK, September 4-7, 2012. Proceedings, volume 7454 of Lecture Notes in Computer Science, pages 193-208. Springer, 2012. Google Scholar
  21. Amir Pnueli and Roni Rosner. On the synthesis of a reactive module. In POPL, pages 179-190. ACM Press, 1989. URL: http://dx.doi.org/10.1145/75277.75293.
  22. Sven Schewe. Solving parity games in big steps. In FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science, 27th International Conference, New Delhi, India, December 12-14, 2007, Proceedings, volume 4855 of Lecture Notes in Computer Science, pages 449-460. Springer, 2007. URL: http://dx.doi.org/10.1007/978-3-540-77050-3_37.
  23. Wolfgang Thomas. On the synthesis of strategies in infinite games. In STACS, pages 1-13, 1995. URL: http://dx.doi.org/10.1007/3-540-59042-0_57.
  24. Michael Ummels. Rational behaviour and strategy construction in infinite multiplayer games. In FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science, 26th International Conference, Kolkata, India, December 13-15, 2006, Proceedings, volume 4337 of Lecture Notes in Computer Science, pages 212-223. Springer, 2006. Google Scholar
  25. Michael Ummels. The complexity of nash equilibria in infinite multiplayer games. In Foundations of Software Science and Computational Structures, 11th International Conference, FOSSACS 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29 - April 6, 2008. Proceedings, volume 4962 of Lecture Notes in Computer Science, pages 20-34. Springer, 2008. URL: http://dx.doi.org/10.1007/978-3-540-78499-9_3.
  26. Wieslaw Zielonka. Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci., 200(1-2):135-183, 1998. URL: http://dx.doi.org/10.1016/S0304-3975(98)00009-7.
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