A Proof System in Process Algebra for Demand and Supply

Process Algebra for Demand and Supply (shortly, PADS), proposed by Philippou et al., is a process algebra model for the formal analysis of hierarchical scheduling. They introduce a basic notion of supply simulation relation to characterize task's schedulability. In this paper, we first investigate some properties of supply simulation relation. And then based on these properties, we present a proof system for the supply simulation relation in a decomposing-composing way and prove its soundness and completeness with respect to the semantic definition of a supply simulation relation. The soundness and completeness guarantee that the proof system is used to determine whether a task is schedulable by a supply or not.