SMC: Synthesis of Uniform Strategies and Verification of Strategic Ability for Multi-Agent Systems Jerzy Pilecki 1 , Marek A Bednarczyk 2,3 , and Wojciech Jamroga 3,4 1 Systems Research Institute, Polish Academy of Sciences 2 Polish-Japanese Academy of Information Technology 3 Institute of Computer Science, Polish Academy of Sciences 4 Computer Science and Communication, and Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg Abstract. We present a model checking algorithm for a subset of alter- nating-time temporal logic (ATL) with imperfect information and im- perfect recall. This variant of ATL is arguably most appropriate when it comes to modeling and specification of multi-agent systems. The related variant of model checking is known to be theoretically hard (NP- to PSPACE-complete, depending on the assumptions), but very few prac- tical attempts at it have been proposed so far. Our algorithm searches through the set of possible uniform strategies, utilizing a simple tech- nique that reduces the search space. In consequence, it does not only verify existence of a suitable strategy but also produces one (if it exists). We validate the algorithm experimentally on a simple scalable class of models, with promising results. We also discuss two variants of the model checking problem, related to the objective vs. subjective interpretation of strategic ability. We provide algorithms for reductions between the two semantic variants of model checking. The algorithms are experimentally validated as well. Keywords: model checking, alternating-time logic, imperfect information, strat- egy synthesis 1 Introduction There is a growing number of works that study syntactic and semantic vari- ants of strategic logics, in particular the alternating-time temporal logic ATL. Conceptually, the most interesting strand builds upon reasoning about tempo- ral patterns and outcomes of strategic play, limited by information available to the agents. The contributions are mainly theoretical, and include results con- cerning the conceptual soundness of a given semantics of ability [32, 15, 2, 18], meta-logical properties [9], and the complexity of model checking [32, 17, 16]. However, there is very little research on actual use of the logics, in particular on practical algorithms for reasoning and/or verification.