Algebraic Specification of Resource-Constrained Processes

Abstract: The object of this paper is to design a theoretical framework for the algebraic specification of resource constraints. It is, insofar, intended to provide an extension of the process algebra as introduced by Bergstra & Klop (1982) as well as a formal basis for a coherent theory of the RCPS (resource-constrained project/process scheduling). First, we will give an overview of the axioms and the fundamental terminology of basic process algebra (BPA), namely sequence and alternative. Furthermore, we aquaint the reader with the concept of the (extended) process algebra (PA): interleaving via the so-called merge operator. Then, we introduce new operators and axioms into the process algebra to express and to treat restrictions on concurrent processes competing for the same resource(s). This leads us to the RCPA (resource-constrained process algebra). The aim is to generate all alternatives that do not violate any of the constraints imposed. We conclude our work describing the as yet unsolved problems on the way to a co-herent theory covering all aspects of the RCPS, mainly the integration of a time com-ponent into the algebra