On the Minimal Revision Problem of Specification Automata

Abstract

As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the requirements are expressed as temporal logic specifications. However, in real-life scenarios, it is to be expected that not all user task requirements can be realized by the robot. In such cases, the robot must provide feedback to the user on why it cannot accomplish a given task. Moreover, the robot should indicate what tasks it can accomplish which are as "close" as possible to the initial user intent. This paper establishes that the latter problem, which is referred to as the minimal specification revision problem, is NP complete. A heuristic algorithm is presented that can compute good approximations to the Minimal Revision Problem (MRP) in polynomial time. The experimental study of the algorithm demonstrates that in most problem instances the heuristic algorithm actually returns the optimal solution. Finally, some cases where the algorithm does not return the optimal solution are presented.