Skip to main content

Bounded Synthesis for Petri Games

  • Chapter
  • First Online:
Correct System Design

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This research was partially supported by the German Research Council (DFG) in the Transregional Collaborative Research Center SFB/TR 14 AVACS.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Finkbeiner, B., Schewe, S.: Uniform distributed synthesis. In: Proc. LICS, pp. 321–330. IEEE Computer Society Press (2005)

    Google Scholar 

  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

    Article  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  13. Kupferman, O., Vardi, M.Y.: Synthesizing distributed systems. In: Proc. LICS, pp. 389–398. IEEE Computer Society Press (2001)

    Google Scholar 

  14. Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. JSAT 7(2–3), 71–76 (2010)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  17. Mangassarian, H.: QBF-based formal verification: Experience and perspectives. JSAT 133–191

    Google Scholar 

  18. Pnueli, A., Rosner, R.: Distributed reactive systems are hard to synthesize. In: Proc. FOCS 1990, pp. 746–757 (1990)

    Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  21. Zielonka, W.: Asynchronous automata. In: Rozenberg, G., Diekert, V. (eds.) Book of Traces, pp. 205–248. World Scientific (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bernd Finkbeiner .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Finkbeiner, B. (2015). Bounded Synthesis for Petri Games. In: Meyer, R., Platzer, A., Wehrheim, H. (eds) Correct System Design. Lecture Notes in Computer Science(), vol 9360. Springer, Cham. https://doi.org/10.1007/978-3-319-23506-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23506-6_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23505-9

  • Online ISBN: 978-3-319-23506-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics