Performance preorder and competitive equivalence

Abstract.

A preorder based on execution speed, called performance preorder, is introduced for a simple process algebra with durational actions. Two processes $E$ and $F$ are related -$E \sqsubseteq_p F$- if they have the same functionality (in this case, we have chosen strong bisimulation equivalence) and $E$ is at least as fast as $F$. Hence, this preorder supports the stepwise refinement “from specification to implementation” by increasing efficiency while retaining the same functionality. We show that the problem of finding faster implementations for a specification is connected to the problem of finding more distributed implementations of the same specification. Both performance preorder and the induced equivalence, called competitive equivalence, are provided with sound and complete axiomatizations for finite agents.