Model Checking Dynamic Strategy Logic with Memoryless Strategies

Recently, strategy specification and verification has been an active research direction in many areas, such as multi-agent systems, artificial intelligence, formal methods, logic, and so on. Since alternating-time temporal logic (ATL/ATL*) was proposed by Alur et al., many strategic logics, which are based on ATL/ATL*, have been introduced by many researchers. Among them strategy logic (SL) is an outstanding representative, which can express more properties like the existence of Nash Equilibrium in game theory; however, it cannot express regular temporal properties, nor epistemic properties. Based on linear dynamic logic (LDL), we propose a new strategic logic with knowledge, by extending SL. Moreover, under the semantics of memoryless strategies, we show that the model checking problem for this logic is PSPACE-complete with both the length of the sentence and the size of the model.