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Synthesis with Identifiers

  • Rüdiger Ehlers
  • Sanjit A. Seshia
  • Hadas Kress-Gazit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8318)

Abstract

We consider the synthesis of reactive systems from specifications with identifiers. Identifiers are useful to parametrize the input and output of a reactive system, for example, to state which client requests a grant from an arbiter, or the type of object that a robot is expected to fetch.

Traditional reactive synthesis algorithms only handle a constant bounded range of such identifiers. However, in practice, we might not want to restrict the number of clients of an arbiter or the set of object types handled by a robot a priori. We first present a concise automata-based formalism for specifications with identifiers. The synthesis problem for such specifications is undecidable. We therefore give an algorithm that is always sound, and complete for unrealizable safety specifications. Our algorithm is based on computing a pattern-based abstraction of a synthesis game that captures the realizability problem for the specification. The abstraction does not restrict the possible solutions to finite-state ones and captures the obligations for the system in the synthesis game. We present an experimental evaluation based on a prototype implementation that shows the practical applicability of our algorithm.

Keywords

Synthesis Problem Winning Strategy Decision Sequence Menu Item Winning Condition 
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.

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References

  1. 1.
    Attie, P.C., Emerson, E.A.: Synthesis of concurrent systems with many similar processes. ACM Trans. Program. Lang. Syst. 20(1), 51–115 (1998)CrossRefGoogle Scholar
  2. 2.
    Becker, B., Ehlers, R., Lewis, M., Marin, P.: ALLQBF solving by computational learning. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 370–384. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Biere, A.: Picosat essentials. JSAT 4(2-4), 75–97 (2008)zbMATHGoogle Scholar
  4. 4.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Generalized parity games. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 153–167. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Cheng, C.H., Lee, E.A.: Numerical LTL synthesis for cyber-physical systems. CoRR abs/1307.3722 (2013)Google Scholar
  6. 6.
    Dimitrova, R., Finkbeiner, B.: Abstraction refinement for games with incomplete information. In: FSTTCS, pp. 175–186 (2008)Google Scholar
  7. 7.
    Henzinger, T.A., Jhala, R., Majumdar, R.: Counterexample-guided control. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 886–902. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Jacobs, S., Bloem, R.: Parameterized synthesis. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 362–376. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Klieber, W., Janota, M., Marques-Silva, J., Clarke, E.: Solving QBF with free variables. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 415–431. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Kupferman, O., Piterman, N., Vardi, M.Y.: Safraless compositional synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Martin, D.A.: A purely inductive proof of Borel determinacy. In: Recursion theory, Symposium on Pure Mathematics, pp. 303–308 (1982)Google Scholar
  12. 12.
    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
  13. 13.
    Tabuada, P.: Verification and Control of Hybrid Systems. Springer (2009)Google Scholar
  14. 14.
    Walukiewicz, I.: Pushdown processes: Games and model-checking. Inf. Comput. 164(2), 234–263 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Wolper, P.: Expressing interesting properties of programs in propositional temporal logic. In: POPL, pp. 184–193. ACM Press (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Rüdiger Ehlers
    • 1
    • 2
    • 3
  • Sanjit A. Seshia
    • 1
  • Hadas Kress-Gazit
    • 2
  1. 1.University of California at BerkeleyBerkeleyUnited States
  2. 2.Cornell UniversityIthacaUnited States
  3. 3.University of KasselGermany

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