Perturbed Timed Automata

We consider timed automata whose clocks are imperfect. For a given perturbation error 0<e<1, the perturbed language of a timed automaton is obtained by letting its clocks change at a rate within the interval [1−e,1+e]. We show that the perturbed language of a timed automaton with a single clock can be captured by a deterministic timed automaton. This leads to a decision procedure for the language inclusion problem for systems modeled as products of 1-clock automata with imperfect clocks. We also prove that determinization and decidability of language inclusion are not possible for multi-clock automata, even with perturbation.

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