Vineet Gupta, Thomas A. Henzinger, and Radha Jagadeesan
We define robust timed automata, which are timed automata that accept all trajectories "robustly": if a robust timed automaton accepts a trajectory, then it must accept neighboring trajectories also; and if a robust timed automaton rejects a trajectory, then it must reject neighboring trajectories also. We show that the emptiness problem for robust timed automata is still decidable, by modifying the region construction for timed automata. We then show that, like timed automata, robust timed automata cannot be determinized. This result is somewhat unexpected, given that in temporal logic, the removal of real-time equality constraints is known to lead to a decidable theory that is closed under all boolean operations.
Proceedings of the International Workshop on Hybrid and Real-Time Systems (HART), Lecture Notes in Computer Science 1201, Springer, 1997, pp. 331-345.