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Summary: Perturbed Timed Automata ?
Rajeev Alur 1 , Salvatore La Torre 2 , and P. Madhusudan 3
1 University of Pennsylvania
2 Universita degli Studi di Salerno
3 University of Illinois at Urbana-Champaign
Abstract. We consider timed automata whose clocks are imperfect. For
a given perturbation error 0 < " < 1, the perturbed language of a timed
automaton is obtained by letting its clocks change at a rate within the
interval [1 "; 1 + "]. 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 inclu-
sion 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.
1 Introduction
Traditional automata do not admit an explicit modeling of time and consequently
timed automata [1] were introduced as a formal notation to model the behavior
of real-time systems. Timed automata are nite automata extended with real-
valued variables called clocks , whose vertices and edges are annotated with clock
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