Process algebra with timing: Real time and discrete time

Abstract

We present real time and discrete time versions of ACP with absolute timing and relative timing. The startingpoint is a new real time version 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 ACPdat and ACPdrt. The principal version is an extension of ACPsat 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.