Synthesis with Identifiers
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 ConditionPreview
Unable to display preview. Download preview PDF.
References
- 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.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.Biere, A.: Picosat essentials. JSAT 4(2-4), 75–97 (2008)zbMATHGoogle Scholar
- 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.Cheng, C.H., Lee, E.A.: Numerical LTL synthesis for cyber-physical systems. CoRR abs/1307.3722 (2013)Google Scholar
- 6.Dimitrova, R., Finkbeiner, B.: Abstraction refinement for games with incomplete information. In: FSTTCS, pp. 175–186 (2008)Google Scholar
- 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.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.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.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.Martin, D.A.: A purely inductive proof of Borel determinacy. In: Recursion theory, Symposium on Pure Mathematics, pp. 303–308 (1982)Google Scholar
- 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.Tabuada, P.: Verification and Control of Hybrid Systems. Springer (2009)Google Scholar
- 14.Walukiewicz, I.: Pushdown processes: Games and model-checking. Inf. Comput. 164(2), 234–263 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
- 15.Wolper, P.: Expressing interesting properties of programs in propositional temporal logic. In: POPL, pp. 184–193. ACM Press (1986)Google Scholar