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Decision problems for lower/upper bound parametric timed automata

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Abstract

We investigate a class of parametric timed automata, called lower bound/upper bound (L/U) automata, where each parameter occurs in the timing constraints either as a lower bound or as an upper bound. For such automata, we show that basic decision problems, such as emptiness, finiteness and universality of the set of parameter valuations for which there is a corresponding infinite accepting run of the automaton, is Pspace-complete. We extend these results by allowing the specification of constraints on parameters as a linear system. We show that the considered decision problems are still Pspace-complete, if the lower bound parameters are not compared with the upper bound parameters in the linear system, and are undecidable in general. Finally, we consider a parametric extension of \(\mathsf{MITL}\) 0,∞, and prove that the related satisfiability and model checking (w.r.t. L/U automata) problems are Pspace-complete.

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Authors and Affiliations

  1. Università dell’Insubria, Via Valleggio 11, 22100, Como, Italy

    Laura Bozzelli

  2. Università di Salerno, Via Ponte Don Melillo, 84084, Fisciano, Italy

    Salvatore La Torre

Authors
  1. Laura Bozzelli
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  2. Salvatore La Torre
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Corresponding author

Correspondence to Laura Bozzelli.

Additional information

This research was partially supported by the MIUR grants ex-60% 2006 and 2007 Università di Salerno.

A preliminary version of this paper appears in the Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP’07), LNCS 4596, pp 925–936. Springer, 2007.

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Bozzelli, L., La Torre, S. Decision problems for lower/upper bound parametric timed automata. Form Methods Syst Des 35, 121–151 (2009). https://doi.org/10.1007/s10703-009-0074-0

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  • DOI: https://doi.org/10.1007/s10703-009-0074-0

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