Petri Nets over Partial Algebra

Partial algebra is a suitable tool to define sequential semantics for arbitrary restrictions of the occurrence rule, such as capacity or context restrictions. This paper focuses on non-sequential process semantics of Petri nets over partial algebras. It is shown that the concept of partial algebra is suitable as a basis for process construction of different classes of Petri nets taking dependencies between processes that restrict concurrent composition into consideration.Thus, Petri nets over partial algebra provide a unifying framework for Petri net classes in which some processes cannot be executed concurrently, such as elementary nets with context. We will illustrate this claim proving a one-to-one correspondence between processes constructed using partial algebra and processes based on partial orders for elementary nets with context. Furthermore, we provide compositional process term semantics using the presented framework for place/transition nets with (both weak and strong) capacities and place/transition nets with inhibitor arcs.