Abstract
We propose a logic for the definition of the collaborative power of groups of agents to enforce different temporal objectives. The resulting temporal cooperation logic (TCL) extends ATL by allowing for successive definition of strategies for agents and agencies. Different to previous logics with similar aims, our extension cuts a fine line between extending the power and maintaining a low complexity: model-checking TCL sentences is EXPTIME complete in the logic, and fixed parameter tractable for specifications of bounded size. This advancement over non-elementary logics is bought by disallowing a too close entanglement between cooperation and competition. We show how allowing such an entanglement immediately leads to a non-elementary complexity. We have implemented a model-checker for the logic and shown the feasibility of model-checking on a few benchmarks.
The research was supported by the National Science Council grant 97-2221-E-002-129-MY3 and by the Engineering and Physical Sciences Research Council grant EP/H046623/1.
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References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM (JACM) 49(5), 672–713 (2002)
Axelrod, R.: Effective choice in the prisoner’s dilemma. Journal of Conflict Resolution 24(1), 3–25 (1980)
Baier, C., Brázdil, T., Gröser, M., Kucera, A.: Stochastic game logic. In: QEST, pp. 227–236. IEEE Computer Society (2007)
Büchi, J., Landweber, L.: Definability in th emonadic second-order theory of successor. Journal of Symbolic Logic 34(2), 166–170 (1969)
Büchi, J., Landweber, L.: Solving sequential conditions by finite-state strategies. Trans. AMS 138(4), 295–311 (1969)
Chatterjee, K., Henzinger, M.: An O(n 2) time algorithm for alternating Büchi games. In: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012), Kyoto, Japan, January 17-19, pp. 1386–1399. SIAM (2012)
Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Information and Computation 208, 677–693 (2010)
Clarke, E.M., Emerson, E.A.: Design and Synthesis of Synchronization Skeletons Using Branching-time Temporal Logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)
Costa, A.D., Laroussinie, F., Markey, N.: Atl with strategy contexts: Expressiveness and model checking. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), vol. 8, pp. 120–132. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2010)
Finkbeiner, B., Schewe, S.: Coordination Logic. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 305–319. Springer, Heidelberg (2010)
Holzmann, G.J.: The model checker spin. IEEE Trans. Software Eng. 23(5) (1997)
Immerman, N.: Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences 22(3), 65–72 (1981)
Kupferman, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. Journal of ACM 47(2), 312–360 (2000)
Mogavero, F., Murano, A., Perelli, G., Vardi, M.Y.: What Makes Atl* Decidable? A Decidable Fragment of Strategy Logic. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 193–208. Springer, Heidelberg (2012)
Mogavero, F., Murano, A., Vardi, M.Y.: Reasoning about strategies. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). LIPIcs, vol. 8, pp. 133–144 (2010)
Muller, D.E., Schupp, P.E.: Simulating alternating tree automata by nondeterministic automata: new results and new proofs of the theorems of Rabin, McNaughton and Safra. Theoretical Computer Science 141(1-2), 69–107 (1995)
Pnueli, A.: The temporal logic of programs. In: 18th Annual IEEE-CS Symposium on Foundations of Computer Science, pp. 45–57 (1977)
Schewe, S.: Solving Parity Games in Big Steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007)
Stockmeyer, L.J., Chandra, A.K.: Provably difficult combinatorial games. SIAM Journal on Computing (SICOMP) 8(2), 151–174 (1979)
Vardi, M., Stockmeyer, L.: Improved upper and lower bounds for modal logics of programs: Preliminary report. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing (STOC 1985), Providence, Rhode Island, USA, May 6-8, pp. 240–251 (1985)
Wang, F., Huang, C.-H., Yu, F.: A Temporal Logic for the Interaction of Strategies. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 466–481. Springer, Heidelberg (2011)
Wilke, T.: Alternating tree automata, parity games, and modal μ-calculus. Bulletin of the Belgian Mathematical Society 8(2) (May 2001)
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Huang, CH., Schewe, S., Wang, F. (2013). Model-Checking Iterated Games. In: Piterman, N., Smolka, S.A. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2013. Lecture Notes in Computer Science, vol 7795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36742-7_11
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