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Article Dans Une Revue Logical Methods in Computer Science Année : 2008

On the Expressiveness and Complexity of ATL

Résumé

ATL is a temporal logic geared towards the specification and verification of properties in multi-agents systems. It allows to reason on the existence of strategies for coalitions of agents in order to enforce a given property. We prove that the standard definition of~ATL (built on modalities "Next", "Always" and~"Until") has to be completed in order to express the duals of its modalities: it~is necessary to add the modality "Release". We~then precisely characterize the complexity of ATL model-checking when the number of agents is not fixed. We prove that it is \(Δ_2^P\) and \(Δ_3^P\)-complete, depending on the underlying multi-agent model (ATS and CGS,~resp.). We also prove that~ATL\(^+\) model-checking is \(Δ_3^P\)-complete over both models, even with a fixed number of agents.
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Dates et versions

hal-01194598 , version 1 (07-09-2015)

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François Laroussinie, Nicolas Markey, Ghassan Oreiby. On the Expressiveness and Complexity of ATL. Logical Methods in Computer Science, 2008, 4 (2\string:7), pp.1. ⟨10.2168/LMCS-4(2:7)2008⟩. ⟨hal-01194598⟩
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