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

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