Reachability in Timed Counter Systems

We introduce Timed Counter Systems, a new class of systems mixing clocks and counters. Such systems have an infinite state space, and their reachability problems are generally undecidable. By abstracting clock values with a Region Graph, we show the Counter Reachability Problem to be decidable for three subclasses: Timed VASS, Bounded Timed Counter Systems, and Reversal-Bounded Timed Counter Systems.