Petri net semantics of priority systems

The specification of priorities provides a convenient way of resolving conflicts in the design of concurrent computing systems. Priorities have been widely used by operating systems to enforce the preferred order of the execution of jobs waiting for processing; while programming languages often provide primitives, such as prioritised choice operator, for expressing the intended preference of the execution of one enabled section of the program over another enabled section of the program.In this paper we consider priority systems (Σ, ϱ), where Σ is a bounded Petri net, and ϱ is a priority relation on the transitions of the net. Our main goal is to give a formal semantics of (Σ, ϱ) by constructing a Petri net Σϱ which would retain as much of the concurrency semantics of Σ as possible and at the same time not violate the priority constraints imposed by ϱ. In the construction provided by this paper, Σϱ is derived from Σ by adding additional places and arcs, and by splitting the transitions of the original net Σ if necessary. The way in which these new places are added generalises the standard complementation technique introduced for P/T-nets. For safe nets Σ he construction can be simplified and Σϱ built without splitting of any transitions. We then outline how the translation from (Σ, ϱ) to Σϱ might be used to give a formal semantics of the prioritised choice operator.