Discrete time process algebra

Abstract

The axiom system ACP of [BEK84aJ was extended with real time features in [BAB91 J. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NIS94J. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. The time free ACP theory is embedded in the discrete time theory.

Algebra of timed frames

“…[lo]). The result further implies that the operational semantics given in [6] could be simplified considerably at the expense of a more complicated notion of bisimulation, viz. a-bisimulation.…”

“…We will also make use of the initialization operator >; . and the initial abstraction operator 4, for discrete time as in [6]. The process n >> P is the absolute time process obtained by initializing relative (or parametric) time process P at absolute time n, and J,x.…”

“…We will make use of a discrete time extension of BPA (Basic Process Algebra) for relative time presented in [6], viz. BPA;,.…”

“…We study the connection between timed frames and discrete time processes in the setting of the discrete time extensions of ACP described in [6]. The primary motivation of this study is logic based: a better understanding of the connection facilitates a systematic approach to devise a suitable logic for reasoning about discrete time processes, applying techniques from modal logic (relevant examples of the application of these techniques can be found in [7,8]).…”

“…Time determinism, the property that passage of time by itself can not determine a choice, is built into the operational semantics of the versions of discrete time process algebra presented in [6] by preventing that states with more than one outgoing time step occur. An alternative is used here for timed frames: a special kind of bisimulation, called a-bisimulation, sees to that passage of time by itself can not determine a choice.…”