Section: New Results

Occurrence net Synthesis

Occurrence nets are a well known partial order model for the concurrent behavior of Petri nets. The causality and conflict relations between events, which are explicitly represented in occurrence nets, induce logical dependencies between event occurrences: the occurrence of an event e in a run implies that all its causal predecessors also occur, and that no event in conflict with e occurs. But these structural relations do not express all the logical dependencies between event occurrences in maximal runs: in particular, the occurrence of e in any maximal run may imply the occurrence of another event that is not a causal predecessor of e, in that run. The reveals relation had been introduced in [33] to express this dependency between two events. In this work, presented at ACSD 2011 [44] , we extend the theory in two ways : first, wegeneralize the reveals relation to express more general dependencies, involving more than two events, and we introduce ERL logic to express these dependencies as boolean formulas. Secondly, we solve the synthesis problem that arises: given an ERL formula $\phi$, is there a finite occurrence net $𝒩$ such that $\phi$ describes exactly the dependencies between the events of $𝒩$ ? The resulting method requires only two synthesis rules.