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 (SIGMA, rho), where SIGMA is a bounded Petri net, and rho is a priority relation on the transitions of the net. Our main goal is to give a formal semantics of (SIGMA, rho) by constructing a Petri net SIGMA(rho) which would retain as much of the concurrency semantics of SIGMA as possible and at the same time not violate the priority constraints imposed by rho. In the construction provided by this paper, SIGMA(rho) is derived from SIGMA by adding additional places and arcs, and by splitting the transitions of the original net SIGMA if necessary. The way in which these new places are added generalises the standard complementation technique introduced for P/T-nets. For safe nets SIGMA he construction can be simplified and SIGMA(rho) built without splitting of any transitions. We then outline how the translation from (SIGMA, rho) to SIGMA(rho) might be used to give a formal semantics of the prioritised choice operator.