Abstract
We study the decidability and complexity of the reachability problem in parametric timed automata. The problem was introduced 20 years ago by Alur, Henzinger, and Vardi in [1], where they showed decidability in the case of a single parametric clock, and undecidability for timed automata with three or more parametric clocks.
By translating such problems as reachability questions in certain extensions of parametric one-counter machines, we show that, in the case of two parametric clocks (and arbitrarily many nonparametric clocks), reachability is decidable for parametric timed automata with a single parameter, and is moreover PSPACE NEXP-hard. In addition, in the case of a single parametric clock (with arbitrarily many nonparametric clocks and arbitrarily many parameters), we show that the reachability problem is NEXP-complete, improving the nonelementary decision procedure of Alur et al.
Full version of the paper is available at: http://www.cs.ox.ac.uk/people/joel.ouaknine/publications/advances_parametric14abs.html
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Bundala, D., Ouaknine, J. (2014). Advances in Parametric Real-Time Reasoning. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_11
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DOI: https://doi.org/10.1007/978-3-662-44522-8_11
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