This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebr...

An extension of process algebra is introduced which can be compared to (propositional) dynamic logic. The additional feature is a ‘guard’ construct, related to the notion of a test in dynamic logic. This extension of process algebra is semantically based on processes that transform data, and its operational semantics is defined relative to a structure describing these transformations via transi...

In ACP-style process algebra, the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, different forms of termination can be distinguished: some time termination, current time slice termination, urgent termination, termination in a virtual state. In a setting with the silent action τ , we also have silent termination. This leads to pro...

This paper introduces autonomous observable actions into process algebra. These actions can be observed but cannot be controlled by an environment. The proposed extension of ACP allows verifications without silent steps and fairness assumptions. The inclusion of inequalities makes it possible to verify that an implementation satisfies a given specification, with the specification indicating exa...

In process algebras such as ACP, parallel processes are considered to be interleaved in an arbitrary way. In the case of multi-threading as found in contemporary programming languages, parallel processes are actually interleaved according to some interleaving strategy. Interleaving strategies are also known as process-scheduling policies. In many systems, for instance hardware/software systems,...

We explicitly model entanglement in quantum processes by treating entanglement as a kind of parallelism. We introduce a shadow constant quantum operation and a so-called entanglement merge into quantum process algebra qACP. The transition rules of the shadow constant quantum operation and entanglement merge are designed. We also do a sound and complete axiomatization modulo the so-called quantu...

Published results show that various models may be obtained by combining parallel composition with probability and with or without non-determinism. In this paper we treat this problem in the setting of process algebra in the form of ACP. First, probabilities are introduced by an operator for the internal probabilistic choice. In this way we obtain the Basic Process Algebra with probabilistic cho...

A Hoare-like logic is introduced for deriving`partial correctness assertions' of the form fg p fg, where ; are unary predicates over some state space S and p is an expression over a recursive, non-uniform language containing global nondeterminism (+) and sequential composition (). This logic is (relatively) complete if only guarded recursion is considered.

An unbounded queue over a finite set of data 1is,,a Q. in -.A defined by an infinite system of guarded equations. The aim of this paper is to show that no finite system of guarded equations is capable of defining Q. This is a revised version of: Process algebra semantics for queues, Mathematical Centre Research Report IW241,, Amst,rdam.,1983.. * present affiliation & correspondence address: of ...

The objective of this paper is to bridge the gap between ACP and TCSP. To this end, ACP is extended with two non-deterministic choice operators in a setting of bisimulation semantics. With these operators, we can express safety properties of systems without the use of silent steps, and we can verify safety properties in a setting in which no assumption on fairness (or unfairness) has been made.