Model-checking iterated games

Huang, Chung-Hao; Schewe, Sven; Wang, Farn

doi:10.1007/s00236-016-0277-y

Cited by 2 publications

(1 citation statement)

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“…Several works have focused on extensions of ATL and ATL * to incorporate more powerful strategic constructs. Among them, we recall alternating-time μCALCULUS (AμCALCULUS) [Alur et al 2002], game logic (GL) [Alur et al 2002], quantified decision modality μCALCULUS (QDμCALCULUS) [Pinchinat 2007], coordination logic (CL) [Finkbeiner and Schewe 2010], ATLwith plausibility (ATL + ) [Bulling et al 2008], ATLwith Irrevocable strategies (IATL) [Agotnes et al 2007], memoryful ATL * (mATL * ) [Mogavero et al 2010b], basic strategy-interaction logic (BSIL) [Wang et al 2011], temporal Cooperation Logic (TCL) [Huang et al 2013], alternating-time temporal logic with explicit actions (ATLEA) [Herzig et al 2013], and some extensions of ATL * considered in Brihaye et al [2009]. AμCALCULUS and QDμCALCULUS are intrinsically different from SL (as well as from CHP-SL and ATL * ), as they are obtained by extending the propositional μ-calculus [Kozen 1983] with strategic modalities.…”

Section: Introductionmentioning

confidence: 99%

Reasoning About Strategies

Mogavero

Murano

Perelli

et al. 2014

ACM Trans. Comput. Logic

138

155

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In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multiagent games, such as ATL, ATL * , and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a nonelementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multiagent systems.In this article, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multiagent concurrent games. As a key aspect, strategies in SL are not intrinsically glued to a specific agent, but an explicit binding operator allows an agent to bind to a strategy variable. This allows agents to share strategies or reuse one previously adopted. We prove that SL strictly includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NONELEMENTARY. This negative result has spurred us to investigate syntactic fragments of SL, strictly subsuming ATL * , with the hope of obtaining an elementary model-checking problem. Among others, we introduce and study the sublogics SL [NG], SL [BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals, and, a single goal at a time. Intuitively, for a goal, we mean a sequence of bindings, one for each agent, followed by an LTL formula. We prove that the model-checking problem for SL[1G] is 2EXPTIME-COMPLETE, thus not harder than the one for ATL * . In contrast, SL[NG] turns out to be NONELEMENTARY-HARD, strengthening the corresponding result for SL. Regarding SL[BG], we show that it includes CHP-SL and its model-checking is decidable with a 2EXPTIMElower-bound.It is worth enlightening that to achieve the positive results about SL[1G], we introduce a fundamental property of the semantics of this logic, called behavioral, which allows to strongly simplify the reasoning about strategies. Indeed, in a nonbehavioral logic such as SL [BG] and the subsuming ones, to satisfy a formula, one has to take into account that a move of an agent, at a given moment of a play, may depend on the moves taken by any agent in another counterfactual play.

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