Decision Problems for Parametric Timed Automata

Parametric timed automata (PTAs) allow to reason on systems featuring concurrency and timing constraints making use of parameters. Most problems are undecidable for PTAs, including the parametric reachability emptiness problem, i.e., whether at least one parameter valuation allows to reach some discrete state. In this paper, we first exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Second, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses.