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Located Actions in Process Algebra with Timing

Bergstra J.A., Middelburg C.A.

Fundamenta Informaticae

2004

Vol. 61, nr 3,4

183--211

We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a known time-dependent spatial distribution, such as protocols transmitting data via a mobile intermediate station. It is a reformulation of the real space process algebra from Baeten and Bergstra [Formal Aspects of Computing, 5, 1993, 481-529] in a setting with urgent actions. This leads to many simplifications.

Process Algebra with Nonstandard Timing

Middelburg K.A.

Fundamenta Informaticae

2002

Vol. 53, nr 1

55-77

The possibility of two or more actions to be performed consecutively at the same point in time is not excluded in the process algebras from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 10]. 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 nonstandard non-negative real numbers are included in the 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.