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.
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)
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