Synthesis of Nets with Inhibitor Arcs

The synthesis problem for Petri nets consists in the construction of a net system whose behaviour is specified by a given transition system. In this paper we deal with the synthesis of elementary net systems extended with inhibitor arcs, i.e. arcs that test for absence of tokens in a place. We characterize the class of transitions systems corresponding to the sequential execution of these nets, which is a proper extension of the one obtained by the execution of nets without inhibitor arcs. Finally, we try to minimize the number of inhibitor arcs; we look for conditions guaranteeing that an inhibitor arc is really used, i.e. its presence influences the behaviour of the net.