Jcm Jos Baeten

Real time process algebra

We describe an axiom system ACPp that incorporates real timed actions. Many examples are provided in order to explain the intuitive contents of the notation. ACPp is a generalisation of ACP. This implies that some of the axioms have to be relaxed and that ACP can be recovered as a special case from it. The purpose of ACPp is to serve as a specification language for real time systems. The axioms of ACPp explain its operational meaning in an algebraic form.

A brief history of process algebra

This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

Decidability of bisimulation equivalence for process generating context-free languages

A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process Algebra. Hence to each CFG a process can be assigned as solution, which has as its set of finite traces the context-free language (CFL) determined by that CFG. While the equality problem for CFLs is unsolvable, the equality problem for the processes determined by CFGs turns out to be solvable. Here equality on processes is given by a model of process graphs modulo bisimulation equivalence. The proof is given by displaying a periodic structure of the process graphs determined by CFGs. As a corollary of the periodicity a short proof of the solvability of the equivalence problem for simple context-free languages is given.

On the consistency of Koomen's fair abstraction rule

Abstract We construct a graph model for ACP τ , the algebra of communicating processes with silent steps, in which Koomens Fair Abstraction Rule (KFAR) holds, and also versions of the Approximation Induction Principle (AIP) and the Recursive Definition & Specification Principles (RDP&RSP). We use this model to prove that in ACP T (but not in ACP!) each computably recursively definable process is finitely recursively definable.

Axiomatizing probabilistic processes: ACP with generative probabilities

This paper is concerned with finding complete axiomatizations of probabilistic processes. We examine this problem within the context of the process algebra ACP and obtain as our end-result the axiom system prACP I −- , a probabilistic version of ACP which can be used to reason algebraically about the reliability and performance of concurrent systems. Our goal was to introduce probability into ACP in as simple a fashion as possible. Optimally, ACP should be the homomorphic image of the probabilistic version in which the probabilities are forgotten.

Global renaming operators in concrete process algebra

Renaming operators are introduced in concrete process algebra (concrete means that abstraction and silent moves are not considered). Examples of renaming operators are given: encapsulation, pre-abstraction, and localization. We show that renamings enhance the defining power of concrete process algebra by using the example of a queue. We give a definition of the trace set of a process, see when equality of trace sets implies equality of processes, and use trace sets to define the restriction of a process. Finally, we describe processes with actions that have a side effect on a state space and show how to use this for a translation of computer programs into process algebra.

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 starting-point 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.

Process algebra with propositional signals

We consider processes that have transitions labeled with atomic actions, and states labeled with formulas over a propositional logic. These state labels are called signals. A process in a parallel composition may proceed conditionally, dependent on the presence of a signal in the process in parallel. This allows a natural treatment of signal observation.

Process Algebra with Signals and Conditions

Several new operators are introduced on top of the algebra of communicating processes (ACP) from [BK 84] in order to incorporate stable signals in process algebra. Semantically this involves assigning labels to nodes of process graphs in addition to the actions that serve as labels of edges. The labels of nodes are called signals. In combination with the operators of BPA, two signal insertion operators allow to describe each finite tree labeled with actions and signals. In the context of parallel processes there is a new feature connected with signals: the signal observation mechanism. This mechanism is organised on basis of a signal observation function in very much the same way as the communication mechanism of ACP is organised around a communication function. Also, we discuss conditionals on signals and processes, and make much use of them in our examples.

Term-rewriting systems with rule priorities

In this paper we discuss term-rewriting systems with ru/e prioriries, which simply is a partial ordering on the rules. The procedural meaning of such an ordering then is, that the application of a rule of lower priority is allowed only if no rule of higher priority is applicable. The semantics of such a system is discussed. It turns out that the class of all hounded systems indeed has such a semantics.