On the Expressiveness and Complexity of ATL

Laroussinie, François; Markey, Nicolas; Oreiby, Ghassan

doi:10.1007/978-3-540-71389-0_18

Cited by 17 publications

(12 citation statements)

References 22 publications

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“…Every ini can be encoded as an implicit input function, with each ϕj being of polynomial size with respect to the number of interaction symbols (cf. [16]). …”

Section: Modular Interpreted Systemsmentioning

confidence: 93%

“…the size of In). However, we can use, e.g., a construction similar to the one from [16] to represent interaction functions more compactly. DEFINITION 5.…”

Section: Modular Interpreted Systemsmentioning

confidence: 99%

“…m, l and Δ P 3 -complete wrt. n, k, l (k being the number of agents) [3,12,16]. Model checking ATLir is Δ P 2 -complete wrt.…”

Section: Explicit Modelsmentioning

confidence: 99%

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Modular interpreted systems

Jamroga

Ågotnes²

2007

Proceedings of the 6th International Joint Conference on Autonomous Agents and Multiagent Systems

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We propose a new class of representations that can be used for modeling (and model checking) temporal, strategic and epistemic properties of agents and their teams. Our representations borrow the main ideas from interpreted systems of Halpern, Fagin et al.; however, they are also modular and compact in the way concurrent programs are. We also mention preliminary results on model checking alternating-time temporal logic for this natural class of models.

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“…Every ini can be encoded as an implicit input function, with each ϕj being of polynomial size with respect to the number of interaction symbols (cf. [16]). …”

Section: Modular Interpreted Systemsmentioning

confidence: 93%

“…the size of In). However, we can use, e.g., a construction similar to the one from [16] to represent interaction functions more compactly. DEFINITION 5.…”

Section: Modular Interpreted Systemsmentioning

confidence: 99%

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Modular interpreted systems

Jamroga

Ågotnes²

2007

Proceedings of the 6th International Joint Conference on Autonomous Agents and Multiagent Systems

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“…Note that, unlike for CTL, the path operator W (Weak until) is needed for expressing the dual operator for φ 1 U φ 2 [14]. Furthermore, the standard Gφ path operator can be expressed as φ W false.…”

Section: Syntaxmentioning

confidence: 99%

Reasoning about memoryless strategies under partial observability and unconditional fairness constraints

Busard

Pecheur

et al. 2015

Information and Computation

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Alternating-time Temporal Logic is a logic to reason about strategies that agents can adopt to achieve a specified collective goal. A number of extensions for this logic exist; some of them combine strategies and partial observability, some others include fairness constraints, but to the best of our knowledge no work provides a unified framework for strategies, partial observability and fairness constraints. Integration of these three concepts is important when reasoning about the capabilities of agents without full knowledge of a system, for instance when the agents can assume that the environment behaves in a fair way. We present ATLK irF , a logic combining strategies under partial observability in a system with fairness constraints on states. We introduce a model-checking algorithm for ATLK irF by extending the algorithm for a full-observability variant of the logic and we investigate its complexity. We validate our proposal with an experimental evaluation.

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“…CTL [7,20] and LTL [19]) could only deal with one or all the behaviours of the whole system, ATL [2] expresses properties of (executions generated by) behaviours of individual components of the system. ATL has been extensively studied since then, both about its expressiveness and about its verification algorithms [2,10,12]. P. Gardy, P. Bouyer, N.Markey…”

Section: Introductionmentioning

confidence: 99%

Dependences in Strategy Logic

2020

Self Cite

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Strategy Logic (SL) is a very expressive logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express properties of the resulting plays. Such a powerful framework has two drawbacks: first, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula. We study different kinds of dependences, refining the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014], and prove that they give rise to different satisfaction relations. In the setting where strategies may only depend on what they have observed, we identify a large fragment of SL for which we prove model checking can be performed in 2 -EXPTIME.Strategic interactions in ATL. Strategies in ATL are handled in a very limited way, and there are no real strategic interactions in that logic (which, in return, enjoys a polynomial-time model-checking algorithm). Over the last 10 years, various extensions have been defined and studied in order to allow for more interactions [1,6,5,14,21]. Strategy Logic (SL for short) [6,14] is such a powerful approach, in which strategies are first-class objects; formulas can quantify (universally and existentially) over strategies, store those strategies in variables, assign them to players, and express properties of the resulting plays. As a simple example, the existence of a winning strategy for Player A (with objective ϕ A ) against any strategy of Player B would be written asThis makes the logic both expressive and easy to use (at first sight), at the expense of a very high complexity:SL model checking has non-elementary complexity, and satisfiability is undecidable [14,11]. Dependences in Strategy LogicStrategy dependences in SL. It has been noticed in recent works that the nice expressiveness of SL comes with unexpected phenomena. One recently-identified phenomenon [4] is induced by the separation of strategy quantification and strategy assignment: are the events between strategy quantifications and strategy assignments part of the memory of the strategy? While both options may make sense depending on the applications, only one of them makes model checking decidable [4].A second phenomenon-which is the main focus of the present paper-concerns strategy dependences [14]: in a formula such as ∀σ A . ∃σ B . ξ, the existentially-quantified strategy σ B may depend on the whole strategy σ A ; in other terms, the action returned by strategy σ B after some finite history ρ may depend on what strategy σ A would play on any other history ρ . Again, this may be desirable in some contexts, but it may also make sense to require that strategy σ B after history ρ can be computed based solely on what has been observed along ρ. This approach was initiate...

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On the Expressiveness and Complexity of ATL

Cited by 17 publications

References 22 publications

Modular interpreted systems

Modular interpreted systems

Reasoning about memoryless strategies under partial observability and unconditional fairness constraints

Dependences in Strategy Logic

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