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Sampled universality of timed automata. (English) Zbl 1195.68052
Seidl, Helmut (ed.), Foundations of software science and computational structures. 10th international conference, FOSSACS 2007, held as part of the joint European conferences on theory and practice of software, ETAPS 2007, Braga, Portugal, March 24 – April 1, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-71388-3/pbk). Lecture Notes in Computer Science 4423, 2-16 (2007).
Summary: Timed automata can be studied in not only a dense-time setting but also a discrete-time setting. The most common example of discrete-time semantics is the so called sampled semantics (i.e., discrete semantics with a fixed time granularity \(\epsilon )\). In the real-time setting, the universality problem is known to be undecidable for timed automata. In this work, we study the universality question for the languages accepted by timed automata with sampled semantics. On the negative side, we show that deciding whether for all sampling periods \(\epsilon \) a timed automaton accepts all timed words in \(\epsilon \)-sampled semantics is as hard as in the real-time case, i.e., undecidable. On the positive side, we show that checking whether there is a sampling period such that a timed automaton accepts all untimed words in \(\epsilon \)-sampled semantics is decidable. Our proof uses clock difference relations, developed to characterize the reachability relation for timed automata in connection with sampled semantics.
For the entire collection see [Zbl 1116.68009].

68Q45 Formal languages and automata
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