Designing Petri nets with strong place and transition anticipation for real-valued functions

Abstract

We propose extending the classic Petri nets and considering D. Dubois’s strong anticipation in two ways. We propose to add a new term into a transition rule that contains a real-valued function of a new marking in a certain place (strong place anticipation) or of a new marking in the input place of a certain transition (an example of strong transition anticipation). Any integer constraints are not applied either to the weight function or to the marking in contrast to the classic Petri nets (as in continuous Petri nets). The execution of the mentioned nets is investigated, and important properties are stated. Several examples of reachability graphs are given, and differences from classic Petri nets are formulated. We also investigate the conditions of the equality of the markings, which are obtained by firing the sequences of transitions tjtk and tktj.