MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable

Karin Quaas
(University of Leipzig)

Parametric timed automata extend timed automata (Alur and Dill, 1991) in that they allow the specification of parametric bounds on the clock values. Since their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the emptiness problem for parametric timed automata with one clock is decidable, whereas it is undecidable if the automaton uses three or more parametric clocks. The problem is open for parametric timed automata with two parametric clocks. Metric temporal logic, MTL for short, is a widely used specification language for real-time systems. MTL-model checking of timed automata is decidable, no matter how many clocks are used in the timed automaton. In this paper, we prove that MTL-model checking for parametric timed automata is undecidable, even if the automaton uses only one clock and one parameter and is deterministic.

In Étienne André and Goran Frehse: Proceedings 1st International Workshop on Synthesis of Continuous Parameters (SynCoP 2014), Grenoble, France, 6th April 2014, Electronic Proceedings in Theoretical Computer Science 145, pp. 5–17.
Published: 31st March 2014.

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