Abstract
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.
Partially supported by the PAI “Brancusi” no. 08797XL.
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Dima, C. (2005). Timed Shuffle Expressions. In: Abadi, M., de Alfaro, L. (eds) CONCUR 2005 – Concurrency Theory. CONCUR 2005. Lecture Notes in Computer Science, vol 3653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539452_11
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DOI: https://doi.org/10.1007/11539452_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28309-6
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