Abstract
Starting from alternating-time temporal logic, many logics for reasoning about strategies in a system of agents have been proposed. Some of them consider the strategies that agents can play when they have partial information about the state of the system. \(ATLK_{irF}\) is such a logic to reason about uniform strategies under unconditional fairness constraints. While this kind of logics has been extensively studied, practical approaches for solving their model-checking problem appeared only recently. This paper considers three approaches for model-checking strategies under partial observability of the agents, applied to \(ATLK_{irF}\). These three approaches have been implemented in PyNuSMV, a Python library based on the state-of-the-art model checker NuSMV. Thanks to the experimental results obtained with this library and thanks to the comparison of the relative performance of the approaches, this paper provides indications and guidelines for the use of these verification techniques, showing that different approaches are needed in different situations.
Similar content being viewed by others
References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002). https://doi.org/10.1145/585265.585270
Bozianu, R., Dima, C., Filiot, E.: Safraless synthesis for epistemic temporal specifications. In: Biere, A., Bloem, R. (eds.) Computer Aided Verification. Lecture Notes in Computer Science, vol. 8559, pp. 441–456. Springer, Berlin (2014). https://doi.org/10.1007/978-3-319-08867-9_29
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. 100(8), 677–691 (1986)
Bulling, N., Jamroga, W.: Comparing variants of strategic ability: how uncertainty and memory influence general properties of games. Auton. Agents Multi-Agent Syst. 28(3), 474–518 (2014). https://doi.org/10.1007/s10458-013-9231-3
Busard, S.: Symbolic model checking of multi-modal logics: uniform strategies and rich explanations. Ph.D. thesis, Université catholique de Louvain (2017)
Busard, S., Pecheur, C.: PyNuSMV: NuSMV as a Python library. In: Brat, G., Rungta, N., Venet, A. (eds.) Nasa Formal Methods 2013, LNCS, vol. 7871, pp. 453–458. Springer, Berlin (2013)
Busard, S., Pecheur, C., Qu, H., Raimondi, F.: Reasoning about strategies under partial observability and fairness constraints. In: Mogavero, F., Murano, A., Vardi, M.Y. (eds.) Proceedings 1st International Workshop on Strategic Reasoning, SR 2013, Rome, Italy, March 16–17, 2013., EPTCS, vol. 112, pp. 71–79 (2013). https://doi.org/10.4204/EPTCS.112.12
Busard, S., Pecheur, C., Qu, H., Raimondi, F.: Improving the model checking of strategies under partial observability and fairness constraints. In: Merz, S., Pang, J. (eds.) Formal Methods and Software Engineering. Lecture Notes in Computer Science, vol. 8829, pp. 27–42. Springer, Berlin (2014). https://doi.org/10.1007/978-3-319-11737-9_3
Busard, S., Pecheur, C., Qu, H., Raimondi, F.: Reasoning about memoryless strategies under partial observability and unconditional fairness constraints. Inf. Comput. 242, 128–156 (2015). https://doi.org/10.1016/j.ic.2015.03.014
Calta, J., Shkatov, D., Schlingloff, H.: Finding uniform strategies for multi-agent systems. In: Dix, J., Leite, J., Governatori, G., Jamroga, W. (eds.) Computational Logic in Multi-Agent Systems. Lecture Notes in Computer Science, vol. 6245, pp. 135–152. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-14977-1_12
Cavada, R., Cimatti, A., Jochim, C.A., Keighren, G., Olivetti, E., Pistore, M., Roveri, M., Tchaltsev, A.: NuSMV 2.5 User manual
Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV 2: an opensource tool for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) Computer Aided Verification. Lecture Notes in Computer Science, vol. 2404, pp. 359–364. Springer, Berlin (2002). https://doi.org/10.1007/3-540-45657-0_29
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Dastani, M., Jamroga, W.: Reasoning about strategies of multi-agent programs. Proc. AAMAS 10, 997–1004 (2010)
Dima, C., Tiplea, F.L.: Model-checking ATL under imperfect information and perfect recall semantics is undecidable. arXiv:1102.4225 (2011)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)
Huang, X., van der Meyden, R.: An epistemic strategy logic (extended abstract). In: Mogavero, F., Murano, A., Vardi, M.Y. (eds.) Proceedings 2nd International Workshop on Strategic Reasoning, Grenoble, France, April 5–6, 2014, Electronic Proceedings in Theoretical Computer Science, vol. 146, pp. 35–41. Open Publishing Association (2014). https://doi.org/10.4204/EPTCS.146.5
Huang, X., van der Meyden, R.: Symbolic model checking epistemic strategy logic. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, July 27- -31, 2014, Québec City, Québec, Canada., pp. 1426–1432 (2014)
Jamroga, W., Ågotnes, T.: Constructive knowledge: what agents can achieve under imperfect information. J. Appl. Non-Class. Logics 17(4), 423–475 (2007). https://doi.org/10.3166/jancl.17.423-475
Jamroga, W., Dix, J.: Model checking abilities under incomplete information is indeed \(\varDelta ^P_2\)-complete. In: EUMAS’06 (2006)
Jamroga, W., Dix, J.: Model checking abilities of agents: a closer look. Theory Comput. Syst. 42(3), 366–410 (2008). https://doi.org/10.1007/s00224-007-9080-z
Jamroga, W., van der Hoek, W.: Agents that know how to play. Fundam. Inf. 63(2), 185–219 (2004)
Lomuscio, A., Qu, H., Raimondi, F.: MCMAS: an open-source model checker for the verification of multi-agent systems. Int. J. Softw. Tools Technol. Transf. (2015). https://doi.org/10.1007/s10009-015-0378-x
Lomuscio, A., Raimondi, F.: Model checking knowledge, strategies, and games in multi-agent systems. In: 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2006), Hakodate, Japan, May 8–12, 2006, pp. 161–168 (2006). https://doi.org/10.1145/1160633.1160660
Pilecki, J., Bednarczyk, M.A., Jamroga, W.: Synthesis and verification of uniform strategies for multi-agent systems. In: Bulling, N., van der Torre, L., Villata, S., Jamroga, W., Vasconcelos, W. (eds.) Computational Logic in Multi-Agent Systems. Lecture Notes in Computer Science, vol. 8624, pp. 166–182. Springer, Berlin (2014). https://doi.org/10.1007/978-3-319-09764-0_11
Raskin, J., Chatterjee, K., Doyen, L., Henzinger, T.A.: Algorithms for omega-regular games with imperfect information. Logical Methods Comput. Sci. (2007). https://doi.org/10.2168/LMCS-3(3:4)2007
Schobbens, P.Y.: Alternating-time logic with imperfect recall. Electron. NotesTheor. Comput. Sci. 85(2), 82–93 (2004). https://doi.org/10.1016/S1571-0661(05)82604-0
van Ditmarsch, H., Knight, S.: Partial information and uniform strategies. In: Bulling, N., van der Torre, L., Villata, S., Jamroga, W., Vasconcelos, W. (eds.) Computational Logic in Multi-Agent Systems. Lecture Notes in Computer Science, vol. 8624, pp. 183–198. Springer, Berlin (2014). https://doi.org/10.1007/978-3-319-09764-0_12
van Ditmarsch, H., Kooi, B.: One hundred prisoners and a light bulb. In: One Hundred Prisoners and a Light Bulb, pp. 83–94. Springer International Publishing (2015). https://doi.org/10.1007/978-3-319-16694-0_9
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Busard, S., Pecheur, C., Qu, H. et al. Comparing approaches for model-checking strategies under imperfect information and fairness constraints. Int J Softw Tools Technol Transfer 21, 449–469 (2019). https://doi.org/10.1007/s10009-018-0505-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10009-018-0505-6