Global Model Checking on Pushdown Multi-Agent Systems

Pushdown multi-agent systems, modeled by pushdown game structures (PGSs), are an important paradigm of infinite-state multi-agent systems. Alternatingtime temporal logics are well-known specification formalisms for multi-agent systems, where the selective path quantifier is introduced to reason about strategies of agents. In this paper, we investigate model checking algorithms for variants of alternating-time temporal logics over PGSs, initiated by Murano and Perelli at IJCAI’15. We first give a triply exponential-time model checking algorithm for ATL∗ over PGSs. The algorithm is based on the saturation method, and is the first global model checking algorithm with a matching lower bound. Next, we study the model checking problem for the alternating-time μ-calculus. We propose an exponential-time global model checking algorithm which extends similar algorithms for pushdown systems and modal μ-calculus. The algorithm admits a matching lower bound, which holds even for the alternation-free