On the Expressiveness and Complexity of ATL

Abstract

Abstract. 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 ∆ P 2 -and ∆ 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".

Comparing variants of strategic ability: how uncertainty and memory influence general properties of games

“…The former has been focused on the way in which ATL and its extensions can be used for verification of multi-agent systems, in particular what is the complexity of model checking, and how one can overcome the inherent difficulties. An interested reader is referred to [13] for an overview, and to [9,17,20,24,42,48,57,59] for more specific results; some attempts at taming the complexity were proposed e.g. in [18,23,38,46,47].…”

“…Axiomatization of the basic variant of ATL was proposed in [31], and its expressivity was addressed in [9,48]. Axiomatization of a particular variant of imperfect information was proposed in [32].…”

“…The semantics of ATL in concurrent game models was originally proposed for finite structures only [9]. 3 Many follow-up papers also adopted the assumption of finite models, for example [43,57] that studied variants of ATL with imperfect information [11], which extended ATL with persistent strategies, in [48] the expressive power of ATL is investigated, etc.…”

Good Friends are Hard to Find!

“…It is then possible to express controllability properties, such as "Player 1 has a strategy to reach some given state". Compared to CTL, this extension comes with no extra cost: it can still be verified in polynomial time [1] (though there can be slight discrepancies when the number of agents is a parameter [14]). …”

On the Expressiveness and Complexity of ATL

“…Section 3 explains our expressiveness result, and Section 4 deals with the model-checking algorithms. Due to lack of space, some proofs are omitted in this article, but can be found in [13]. …”