ATL Satisfiability is Indeed EXPTIME-complete

The alternating-time temporal logic (ATL) of Alur, Henzinger and Kupferman is being increasingly widely applied in the specification and verification of open distributed systems and game-like multi-agent systems. In this article, we investigate the computational complexity of the satisfiability problem for ATL. For the case where the set of agents is fixed in advance, this problem was settled at EXPTIME-complete in a result of van Drimmelen. If the set of agents is not fixed in advance, then van Drimmelen’s construction yields a 2EXPTIME upper bound. In this article, we focus on the latter case and define three natural variations of the satisfiability problem. Although none of these variations fixes the set of agents in advance, we are able to prove containment in EXPTIME for all of them by means of a type elimination construction—thus improving the existing 2EXPTIME upper bound to a tight