A Turn-Based Approach for Qualitative Time Concurrent Games

We address concurrent games with a qualitative notion of time with parity objectives. This setting allows to express how potential controllers interact with their environment and more specifically includes relevant features: transient states where the environment will eventually act, controller avoiding of an environment action either by an immediate controller action or by masking it, etc. In order to solve the controller synthesis in this framework, we design a linear-time building of a timeless turn-based game and show a close connection between strategies of the controller in the two games. Thus we reduce the synthesis problem to a standard problem of turn-based game with parity objectives establishing as a side effect that pure memoryless strategies are enough for winning. Moreover we introduce permissiveness for safety and reachability games as a criterion to choose between winning strategies and prove that one can compute a most permissive strategy (when it exists) in linear time.