A Holistic State Equation for Timed Petri Nets

Timed Petri nets (TPN) or Duration Petri nets (DPN) is a well-know approach to extend “classic” Petri nets in order to allow the modeling of time [1]. In [2], a state equation for TPN was provided that describes the net’s marking in an algebraic manner, but not its transitions clocks. Hence, proofing the nonreachability of a marking is mainly done by symbolic manipulation of the state equation, which is impractical for the automated generation of such proofs. Here, we introduce a holistic state equation that allows for modeling the clocks algebraically in addition to markings and thus provides a more automatical way to show the nonreachablity of specific markings.