We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to decide realizability and how to perform synthesis. Using a classical result from verification, we show that for specifications in LTL\X, parameterized synthesis of token ring networks is equivalent to distributed synthesis of a network consisting of a few copies of a single process. Adapting a result from distributed synthesis, we show that the latter problem is undecidable. We then describe a semi-decision procedure based on bounded synthesis and show applicability on a simple case study. Finally, we sketch a general framework for parameterized synthesis based on cut-off results for verification.


Model Check Synthesis Problem Label Transition System Parameterized Synthesis Parameterized Architecture 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Church, A.: Logic, arithmetic and automata. In: Proceedings International Mathematical Congress (1962)Google Scholar
  2. 2.
    Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. Symposium on Principles of Programming Languages (POPL 1989), pp. 179–190 (1989)Google Scholar
  3. 3.
    Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of Reactive(1) Designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Specify, compile, run: Hardware form PSL. In: 6th International Workshop on Compiler Optimization Meets Compiler Verification. Electronic Notes in Theoretical Computer Science (2007)Google Scholar
  5. 5.
    Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Automatic hardware synthesis from specifications: A case study. In: Proceedings of the Design, Automation and Test in Europe, pp. 1188–1193 (2007)Google Scholar
  6. 6.
    Katz, G., Peled, D.: Synthesizing Solutions to the Leader Election Problem Using Model Checking and Genetic Programming. In: Namjoshi, K., Zeller, A., Ziv, A. (eds.) HVC 2009. LNCS, vol. 6405, pp. 117–132. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Finkbeiner, B., Jacobs, S.: Lazy Synthesis. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 219–234. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Apt, K., Kozen, D.: Limits for automatic verification of finite-state concurrent systems. Information Processing Letters 22, 307–309 (1986)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Suzuki, I.: Proving properties of a ring of finite state machines. Information processing Letters 28, 213–214 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Emerson, E.A., Namjoshi, K.S.: On reasoning about rings. International Journal of Foundations of Computer Science 14, 527–549 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Clarke, E., Talupur, M., Touili, T., Veith, H.: Verification by Network Decomposition. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 276–291. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Pnueli, A., Rosner, R.: Distributed systems are hard to synthesize. In: Proc. Foundations of Computer Science (FOCS), pp. 746–757 (1990)Google Scholar
  13. 13.
    Finkbeiner, B., Schewe, S.: Uniform distributed synthesis. In: Logic in Computer Science (LICS), pp. 321–330. IEEE Computer Society Press (2005)Google Scholar
  14. 14.
    Schewe, S., Finkbeiner, B.: Synthesis of Asynchronous Systems. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 127–142. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    Finkbeiner, B., Schewe, S.: Bounded synthesis. Software Tools for Technology Transfer (to appear)Google Scholar
  17. 17.
    de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: FOCS, pp. 531–542 (2005)Google Scholar
  19. 19.
    Clarke, E.M., Grumberg, O., Jha, S.: Verifying parameterized networks. ACM Trans. Program. Lang. Syst. 19(5), 726–750 (1997)CrossRefGoogle Scholar
  20. 20.
    Zuck, L.D., Pnueli, A.: Model checking and abstraction to the aid of parameterized systems (a survey). Computer Languages, Systems & Structures 30(3-4), 139–169 (2004)zbMATHCrossRefGoogle Scholar
  21. 21.
    German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Emerson, E.A., Kahlon, V.: Reducing Model Checking of the Many to the Few. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 236–254. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  23. 23.
    Kahlon, V., Ivančić, F., Gupta, A.: Reasoning About Threads Communicating Via Locks. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 505–518. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  24. 24.
    Hanna, Y., Basu, S., Rajan, H.: Behavioral automata composition for automatic topology independent verification of parameterized systems. In: ESEC/SIGSOFT FSE, pp. 325–334 (2009)Google Scholar
  25. 25.
    Kaiser, A., Kroening, D., Wahl, T.: Dynamic Cutoff Detection in Parameterized Concurrent Programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 645–659. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Swen Jacobs
    • 1
  • Roderick Bloem
    • 2
  1. 1.École Polytechnique Fédérale de Lausanne (EPFL)Switzerland
  2. 2.IAIKGraz University of TechnologyAustria

Personalised recommendations