On the semantics of priority systems

A formal definition is presented of the semantics of concurrent systems with priority constraints. It is shown that neither partial orders, which form the basis of several formal semantical theories which explicitly model concurrency, nor total orders, which form the basis of all formal semantical theories which reduce concurrency to arbitrary interleaving, suffice for the treatment of priority. A dialect of COSY, a notation for specifying concurrent systems whose formal semantics is based on partial orders for the treatment of systems in the absence of priorities, is used. A semantical theory of COSY systems including priority constraints, which is based on sequences of multiples is introduced. Finally, it is shown how the concept of starvation can be formally defined in the approach presented.