Theoretical Computer Science
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Journal of Automata, Languages and Combinatorics
Journal of the ACM (JACM)
Decomposition and Composition of Timed Automata
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Renaming is Necessary in Timed Regular Expressions
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Kleene Theorems for Event-Clock Automata
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
A Kleene theorem for timed automata
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Revisiting Digitization, Robustness, and Decidability for Timed Automata
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Undecidability Results for Timed Automata with Silent Transitions
Fundamenta Informaticae
Distributed time-asynchronous automata
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Undecidable problems about timed automata
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Undecidability Results for Timed Automata with Silent Transitions
Fundamenta Informaticae
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We show that stopwatch automata are equivalent to timed shuffle expressions, an extension of timed regular expressions with the shuffle operation. This implies that the emptiness problem for timed shuffle expressions is undecidable. The result holds for both timed state sequence semantics and timed event sequence semantics of automata and expressions.Similarly to timed regular expressions, our timed shuffle expressions employ renaming. But we show that even when renaming is not used, shuffle regular expressions still have an undecidable emptiness problem. This solves in the negative a conjecture of Asarin on the possibility to use shuffle to define timed regular languages.We also define a subclass of timed shuffle expressions which can be used to model preemptive scheduling problems. Expressions in this class are in the form where Ei and E do not use shuffle. We show that emptiness checking within this class is undecidable too.