Inversion of timed Petri nets

A timed Petri net is viewed as an input-output system, where the input is a sequence of transition lifetimes, and the output is the resulting sequence of transitions, markings, and transition epochs. The Petri net is observed via an observation map. The problem of extracting the transition lifetimes is investigated from observations of the output, referred to as inversion. A necessary and sufficient condition for the invertibility of Petri nets is given. For an invertible Petri net, an algorithm to extract the transition lifetimes from the output observations is given. As an application, the problem of structural sensitivity analysis is considered by generating trajectors of perturbed systems with the extract transition lifetimes