Functorial Concurrent Semantics for Petri Nets with Read and Inhibitor Arcs

We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work of Winskel on safe nets, the truly concurrent semantics is given at a categorical level via a chain of functors leading from the category SW-IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains. As an intermediate semantic model, we introduce inhibitor event structures, an extension of prime event structures able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs.