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.


Temporal Logic Production Rule Atomic Proposition Strategy Logic State Formula 
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  1. 1.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM (JACM) 49(5), 672–713 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Axelrod, R.: Effective choice in the prisoner’s dilemma. Journal of Conflict Resolution 24(1), 3–25 (1980)Google Scholar
  3. 3.
    Baier, C., Brázdil, T., Gröser, M., Kucera, A.: Stochastic game logic. In: QEST, pp. 227–236. IEEE Computer Society (2007)Google Scholar
  4. 4.
    Büchi, J., Landweber, L.: Definability in th emonadic second-order theory of successor. Journal of Symbolic Logic 34(2), 166–170 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Büchi, J., Landweber, L.: Solving sequential conditions by finite-state strategies. Trans. AMS 138(4), 295–311 (1969)Google Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Information and Computation 208, 677–693 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)Google Scholar
  10. 10.
    Finkbeiner, B., Schewe, S.: Coordination Logic. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 305–319. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Holzmann, G.J.: The model checker spin. IEEE Trans. Software Eng. 23(5) (1997)Google Scholar
  12. 12.
    Immerman, N.: Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences 22(3), 65–72 (1981)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kupferman, O., Vardi, M.Y., Wolper, P.: An automata-theoretic approach to branching-time model checking. Journal of ACM 47(2), 312–360 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Pnueli, A.: The temporal logic of programs. In: 18th Annual IEEE-CS Symposium on Foundations of Computer Science, pp. 45–57 (1977)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Stockmeyer, L.J., Chandra, A.K.: Provably difficult combinatorial games. SIAM Journal on Computing (SICOMP) 8(2), 151–174 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    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)Google Scholar
  21. 21.
    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)CrossRefGoogle Scholar
  22. 22.
    Wilke, T.: Alternating tree automata, parity games, and modal μ-calculus. Bulletin of the Belgian Mathematical Society 8(2) (May 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Chung-Hao Huang
    • 1
  • Sven Schewe
    • 2
  • Farn Wang
    • 1
    • 3
  1. 1.Graduate Institute of Electronic EngineeringNational Taiwan UniversityTaiwan
  2. 2.Department of Computer SciencesUniversity of LiverpoolUK
  3. 3.Department of Electrical EngineeringNational Taiwan UniversityTaiwan

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