Perturbed timed automata

We consider timed automata whose clocks are imperfect. For a given perturbation error 0 < ε < 1, the perturbed language of a timed automaton is obtained by letting its clocks change at a rate within the interval [1 - ε, 1 + ε]. 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.