Model Checking Pushdown Epistemic Game Structures

In this paper, we investigate the problem of verifying pushdown multiagent systems with imperfect information. As the formal model, we introduce pushdown epistemic game structures (PEGSs), an extension of pushdown game structures with epistemic accessibility relations (EARs). For the specification, we consider extensions of alternating-time temporal logics with epistemic modalities: ATEL, ATEL∗ and AEMC. We study the model checking problems for ATEL, ATEL∗ and AEMC over PEGSs under various imperfect information settings. For ATEL and ATEL∗, we show that size-preserving EARs, a common definition of the accessibility relation in the literature of games over pushdown systems with imperfect information, will render the model checking problem undecidable under imperfect information and imperfect recall setting. We then propose regular EARs, and provide automata-theoretic model checking algorithms with matching low bounds, i.e., EXPTIME-complete for ATEL and 2EXPTIMEcomplete for ATEL∗. In contrast, for AEMC, we show that the model checking problem is EXPTIME-complete even in the presence of size-preserving EARs.