Laroussinie, Francois and Markey, Nicolas and Oreiby, Ghassan - On the Expressiveness and Complexity of ATL

lmcs:826 - Logical Methods in Computer Science, May 15, 2008, Volume 4, Issue 2
On the Expressiveness and Complexity of ATL

Authors: Laroussinie, Francois and Markey, Nicolas and Oreiby, Ghassan

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. In this paper, we first precisely characterize the complexity of ATL model-checking over Alternating Transition Systems and Concurrent Game Structures when the number of agents is not fixed. We prove that it is \Delta^P_2 - and \Delta^P_?_3-complete, depending on the underlying multi-agent model (ATS and CGS resp.). We also consider the same problems for some extensions of ATL. We then consider expressiveness issues. We show how ATS and CGS are related and provide translations between these models w.r.t. alternating bisimulation. We also prove that the standard definition of ATL (built on modalities "Next", "Always" and "Until") cannot express the duals of its modalities: it is necessary to explicitely add the modality "Release".


Source : oai:arXiv.org:0804.2435
DOI : 10.2168/LMCS-4(2:7)2008
Volume: Volume 4, Issue 2
Published on: May 15, 2008
Submitted on: September 20, 2007
Keywords: Computer Science - Logic in Computer Science,Computer Science - Computer Science and Game Theory,Computer Science - Multiagent Systems,F.1.1,F.3.1


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