Model Checking Logics of Strategic Ability: Complexity*

Bulling, Nils; Dix, Jürgen; Jamroga, Wojciech

doi:10.1007/978-1-4419-6984-2_5

Cited by 31 publications

(35 citation statements)

References 33 publications

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“…However, there is relatively little research on the use of the logics, in particular on practical algorithms for reasoning and/or verification in scenarios where agents have a limited view of the world. This is somewhat easy to understand, since model checking of ATL variants with imperfect information has been proved ∆ P 2 -to PSPACE-complete for agents playing memoryless strategies [29,20,5] and EXPTIME-complete to undecidable for agents with perfect recall of the past [13,16]. Moreover, the imperfect information semantics of ATL does not admit alternation-free fixpoint characterizations [6,11,12], which makes incremental synthesis of strategies impossible, or at least difficult to achieve.…”

Section: Introductionmentioning

confidence: 99%

“…There is a growing number of works that study the syntactic and semantic variants of the strategic logic ATL for agents with imperfect information [2]. The contributions are mainly theoretical, and include results concerning the conceptual soundness of a given semantics [29,18,1,21,10,15,2], meta-logical properties [16,7], and the complexity of model checking [29,20,16,30,13,5]. However, there is relatively little research on the use of the logics, in particular on practical algorithms for reasoning and/or verification in scenarios where agents have a limited view of the world.…”

Section: Introductionmentioning

confidence: 99%

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Approximate verification of strategic abilities under imperfect information

Jamroga

Knapik

Kurpiewski

et al. 2019

Artificial Intelligence

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Model checking of strategic ability under imperfect information is known to be hard. The complexity results range from NP-completeness to undecidability, depending on the precise setup of the problem. No less importantly, fixpoint equivalences do not generally hold for imperfect information strategies, which seriously hampers incremental synthesis of winning strategies.In this paper, we propose translations of ATLir formulae that provide lower and upper bounds for their truth values, and are cheaper to verify than the original specifications. That is, if the expression is verified as true then the corresponding formula of ATLir should also hold in the given model. We begin by showing where the straightforward approach does not work. Then, we propose how it can be modified to obtain guaranteed lower bounds. To this end, we alter the next-step operator in such a way that traversing one's indistinguishability relation is seen as atomic activity. Most interestingly, the lower approximation is provided by a fixpoint expression that uses a nonstandard variant of the next-step ability operator. We show the correctness of the translations, establish their computational complexity, and validate the approach by experiments with a scalable scenario of Bridge play.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate verification of strategic abilities under imperfect information

Jamroga

Knapik

Kurpiewski

et al. 2019

Artificial Intelligence

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“…The model checking problem for systems with memoryless strategies and imperfect information against ATL and ATL ⋆ specifications is in PSpace [7]. The algorithm can be adapted to show that the same result applies to SLK.…”

Section: Epistemic Strategy Logicmentioning

confidence: 99%

MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications

Čermák

Lomuscio

Mogavero

et al. 2014

Lecture Notes in Computer Science

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Model checking has come of age. A number of techniques are increasingly used in industrial setting to verify hardware and software systems, both against models and concrete implementations. While it is generally accepted that obstacles still remain, notably handling infinite state systems efficiently, much of current work involves refining and improving existing techniques such as predicate abstraction

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“…The former has been focused on the way in which ATL and its extensions can be used for verification of multi-agent systems, in particular what is the complexity of model checking, and how one can overcome the inherent difficulties. An interested reader is referred to [13] for an overview, and to [9,17,20,24,42,48,57,59] for more specific results; some attempts at taming the complexity were proposed e.g. in [18,23,38,46,47].…”

Section: Related Workmentioning

confidence: 99%

Comparing variants of strategic ability: how uncertainty and memory influence general properties of games

Bulling

Jamroga

2013

Auton Agent Multi-Agent Syst

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Alternating-time temporal logic (ATL) is a modal logic that allows to reason about agents' abilities in game-like scenarios. Semantic variants of ATL are usually built upon different assumptions about the kind of game that is played, including capabilities of agents (perfect vs. imperfect information, perfect vs. imperfect memory, etc.). ATL has been studied extensively in previous years; however, most of the research focused on model checking. Studies of other decision problems (e.g., satisfiability) and formal meta-properties of the logic (like axiomatization or expressivity) have been relatively scarce, and mostly limited to the basic variant of ATL where agents possess perfect information and perfect memory. In particular, a comparison between different semantic variants of the logic is largely left untouched. In this paper, we show that different semantics of ability in ATL give rise to different validity sets. The issue is important for several reasons. First, many logicians identify a logic with its set of true sentences. As a consequence, we prove that different notions of ability induce different strategic logics. Secondly, we show that different concepts of ability induce different general properties of games. Thirdly, the study can be seen as the first systematic step towards satisfiability-checking algorithms for ATL with imperfect information. We introduce sophisticated unfoldings of models and prove invariance results that are an important technical contribution to formal analysis of strategic logics.

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Model Checking Logics of Strategic Ability: Complexity*

Cited by 31 publications

References 33 publications

Approximate verification of strategic abilities under imperfect information

Approximate verification of strategic abilities under imperfect information

MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications

Comparing variants of strategic ability: how uncertainty and memory influence general properties of games

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