Overapproximation of the Number of Active Timers in Timed-Arc Petri Nets Using DP-Systems

Timed-arcs Petri nets are a time extension of Petri nets that allows assigning clocks to tokens. System of dynamic points on a metric graph (DP-systems) is another dynamical model that is studied in discrete geometry dynamics; DP-system combines continuous time and discrete branching events and used, for example, in study of localized Gaussian wave packets scattering on thin structures. In recent works, asymptotic estimates of the growth of the number of points in dynamic systems on metric graphs were obtained. In this paper, we provide a mean to overapproximate the number of different values of timers for a subclass of timed-arc Petri nets by constructing a system of dynamic points on a metric graph and prove overapproximation of the number of timer values by the number of points in the system of dynamic points.