Advertisement

Bounded Synthesis for Petri Games

  • Bernd FinkbeinerEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9360)

Abstract

Petri games, introduced in recent joint work with Ernst-Rüdiger Olderog, are an extension of Petri nets for the causality-based synthesis of distributed systems. In a Petri game, each token is a player in a multiplayer game, played between the “environment” and “system” teams. In this paper, we propose a new technique for finding winning strategies for the system players based on the bounded synthesis approach. In bounded synthesis, we limit the size of the strategy. By incrementally increasing the bound, we can focus the search towards small solutions while still eventually finding every finite winning strategy.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society 138 (1969)Google Scholar
  2. 2.
    Church, A.: Applications of recursive arithmetic to the problem of circuit synthesis. In: Summaries of the Summer Institute of Symbolic Logic, vol. 1, pp. 3–50. Cornell Univ., Ithaca (1957)Google Scholar
  3. 3.
    Copty, F., Fix, L., Fraer, R., Giunchiglia, E., Kamhi, G., Tacchella, A., Vardi, M.Y.: Benefits of bounded model checking at an industrial setting. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 436. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  4. 4.
    Finkbeiner, B., Gieseking, M., Olderog, E.-R.: ADAM: causality-based synthesis of distributed systems. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 433–439. Springer, Heidelberg (2015) CrossRefGoogle Scholar
  5. 5.
    Finkbeiner, B., Olderog, E.: Petri games: synthesis of distributed systems with causal memory. In: Peron, A., Piazza, C. (eds.) Proc. Fifth Intern. Symp. on Games, Automata, Logics and Formal Verification (GandALF). EPTCS, vol. 161, pp. 217–230 (2014). http://dx.doi.org/10.4204/EPTCS.161.19
  6. 6.
    Finkbeiner, B., Schewe, S.: Uniform distributed synthesis. In: Proc. LICS, pp. 321–330. IEEE Computer Society Press (2005)Google Scholar
  7. 7.
    Finkbeiner, B., Schewe, S.: Bounded synthesis. International Journal on Software Tools for Technology Transfer 15(5–6), 519–539 (2013). http://dx.doi.org/10.1007/s10009-012-0228-z CrossRefzbMATHGoogle Scholar
  8. 8.
    Gastin, P., Lerman, B., Zeitoun, M.: Distributed games with causal memory are decidable for series-parallel systems. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 275–286. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  9. 9.
    Genest, B., Gimbert, H., Muscholl, A., Walukiewicz, I.: Asynchronous games over tree architectures. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 275–286. Springer, Heidelberg (2013) Google Scholar
  10. 10.
    Green, C.: Application of theorem proving to problem solving. In: Proceedings of the 1st International Joint Conference on Artificial Intelligence. IJCAI 1969, pp. 219–239. Morgan Kaufmann Publishers Inc., San Francisco (1969). http://dl.acm.org/citation.cfm?id=1624562.1624585
  11. 11.
    Heljanko, K.: Bounded reachability checking with process semantics. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 218–232. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  12. 12.
    Junttila, T.A., Niemelä, I.: Towards an efficient tableau method for boolean circuit satisfiability checking. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 553–567. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  13. 13.
    Kupferman, O., Vardi, M.Y.: Synthesizing distributed systems. In: Proc. LICS, pp. 389–398. IEEE Computer Society Press (2001)Google Scholar
  14. 14.
    Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. JSAT 7(2–3), 71–76 (2010)Google Scholar
  15. 15.
    Madhusudan, P., Thiagarajan, P.S., Yang, S.: The MSO theory of connectedly communicating processes. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 201–212. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  16. 16.
    Madhusudan, P., Thiagarajan, P.S.: Distributed controller synthesis for local specifications. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, p. 396. Springer, Heidelberg (2001) CrossRefGoogle Scholar
  17. 17.
    Mangassarian, H.: QBF-based formal verification: Experience and perspectives. JSAT 133–191Google Scholar
  18. 18.
    Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: Proc. FOCS 1990, pp. 746–757 (1990)Google Scholar
  19. 19.
    Rabin, M.O.: Automata on Infinite Objects and Church’s Problem, Regional Conference Series in Mathematics, vol. 13. Amer. Math. Soc. (1972)Google Scholar
  20. 20.
    Schewe, S., Finkbeiner, B.: Bounded synthesis. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 474–488. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  21. 21.
    Zielonka, W.: Asynchronous automata. In: Rozenberg, G., Diekert, V. (eds.) Book of Traces, pp. 205–248. World Scientific (1995)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Universität des SaarlandesSaarbrückenGermany

Personalised recommendations