We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point isanewrealtimeversion with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete time versions of ACP being known as ACP dat and ACP drt. The principal version is an extension of ACP sat with integration and initial abstraction to allow for choices over an interval of time and relative timing to be expressed. Its main virtue is that it generalizes ACP without timing and most other versions of ACP with timing in a smooth and natural way. This is shown for the real time version with relative timing and the discrete time version with absolute timing.

We propose a variant of the version of branching bisimulation equivalence for processes with discrete relative timing from Baeten, Bergstra, and Reniers. We show that this new equivalence allows for the functional correctness of the PAR protocol as well as its performance properties to be analyzed. The new equivalence still coincides with the original version of branching bisimulation equivalence from van Glabbeek and Weijland in the case without timing.

We prove soundness and completeness for some ACP-style concrete, relative-time, discrete-time process algebras. We treat non-delayable actions, delayable actions, and immediate deadlock. Basic process algebras are examined extensively, and also some concurrent process algebras are considered. We conclude with ACP drt , which combines all described features in one theory. 1991 Mathematics Subject Classification: 68Q10, 68Q22, 68Q55. 1991 CR Categories: D.1.3, D.3.1, F.1.2, F.3.2. Keywords: ACP, process algebra, discrete time, relative time, elimination, soundness, completeness, BPA, BPA # , BPA - drt --#, BPA - drt --ID, BPA drt --ID, BPA - drt , BPA drt , PA - drt --ID, ACP - drt --ID, PA drt , ACP drt , RSP(USD). Note: The investigations of the first author were supported by Philips Research Laboratories Eindhoven, The Netherlands. The investigations of the second author were supported by the Netherlands Computer Science Research Foundation (SION) with financial support from the N...