Probabilistic Alternating-time Temporal Logic and Model Checking Algorithm

Last decade witnesses an impressive development of embedded reactive systems, which motivates the re- search of open systems, where multiple components in- teract with each other and their environment and these interactions decide the behavior of the system. A natu- ral "common-denominator" model for open systems is the concurrent game structure, in which several players can concurrently decide on the behavior of the system. Alternating-time temporal logic (ATL), is a temporal logic geared towards the specification and verification of properties in open systems, which allows to reason on the existence of strategies for coalitions of players in or- der to enforce a given property. Probabilistic systems, i.e. system models where transitions are equipped with random information, receive increasingly attention in recent years. In this paper, we propose to study the open probabilistic system. We extend the framework of ATL in the probabilistic setting, following the style of probabilistic computation tree logic (PCTL), and obtain two probabilistic alternating-time temporal log- ics, i.e. PATL and PATL. They are interpreted over probabilistic concurrent game structures, which is a probabilistic extension of multi-player concurrent game structure. We develop model checking algorithms for both PATL and PATL.