Advances in Parametric Real-Time Reasoning [chapter]

Daniel Bundala, Joël Ouaknine
2014 Lecture Notes in Computer Science  
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
more » ... rarily 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. Notice that every transition in C changes the counter by at most 1. Hence, counter(start(π 2i+1 )) = p r + M + 1 or counter(start(π 2i+1 )) = p r+1 − M − 1.
doi:10.1007/978-3-662-44522-8_11 fatcat:lpm5mihzdrfernwuon6xqgeaxi