Process algebra with nonstandard timing

Abstract

The possibility of two or more actions to be performed consecutively at the same point in time is not excluded in the process algebra from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 101]. This possibility is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. However, it is an abstraction of reality to assume that actions can be performed consecutively at the same point in time. In this paper, we propose a process algebra with timing in which this possibility is excluded, but the finite elements of the nonstandard extension of the non-negative real numbers are taken as time domain. It is shown that this new process algebra generalizes the process algebras with timing from the aforementioned framework in a smooth and natural way.