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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.

Truth of duration calculus formulae in timed frames

Middelburg K.A.

Fundamenta Informaticae

1998

Vol. 36, nr 2,3

235-263

Duration calculus is a logical formalism designed for expressing and refining real-time requirements for systems. Timed frames are essentially transition systems meant for modeling the time-dependent behaviour of programs. We investigate the interpretation of duration calculus formulae in timed frames. We elaborate this topic from different angles and show that they agree with each other. The resulting interpretation is expected to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Such semantic links are prerequisites for a solid underpinning of approaches to system development that cover requirement capture through coding using both duration calculus and some formalism(s) at programming.