Timed Games under Environmental Interference with Real-Time Objectives

Abstract

Classical Timed Games formulations may be unsuitable, or require substantial modeling effort, to capture complex interaction patterns between a controller and its surrounding environment, in which non-determinism must be resolved after the controller has chosen which action to perform. In this paper, we develop the theory of Timed CLTLoc Games (TCGs), a Timed Game variant designed to facilitate the modeling of such patterns. Unlike classical Timed Games formulations, TCGs partition locations rather than transitions, and use Constraint Linear Temporal Logic over clocks (CLTLoc) to specify the controller's objectives. We develop algorithms for solving TCGs and synthesizing winning controller strategies for games whose objectives include formal properties such as reachability and safety. For reachability objectives, our synthesis algorithm yields winning controller strategies that minimize the number of moves required to reach a goal state. Solving reachability TCGs is EXPTIME-complete, matching the complexity of solving reachability Timed Games. All of our algorithms operate backwards and are implemented in our C++ region-based library TARZAN, leveraging OpenMP for efficient parallelization. Experimental results demonstrate the feasibility of TARZAN.