On the Expressiveness and Complexity of ATL [chapter]

François Laroussinie, Nicolas Markey, Ghassan Oreiby
Foundations of Software Science and Computational Structures  
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
more » ... cking when the number of agents is not fixed. We prove that it is Δ P 2 -and Δ P 3 -complete, depending on the underlying multi-agent model (ATS and CGS resp.). We also prove that ATL + model-checking is Δ P 3complete over both models, even with a fixed number of agents. †
doi:10.1007/978-3-540-71389-0_18 dblp:conf/fossacs/LaroussinieMO07 fatcat:hhxmacfvffcqxeavvh2co7d6eu