In search of lost time: Axiomatising parallel composition in process algebras

by   Luca Aceto, et al.

This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus on the recursion, relabelling and restriction free fragment of CCS and we discuss the solutions to three problems that were open for many years. The first problem concerns the status of Bergstra and Klop's auxiliary operators left merge and communication merge in the finite axiomatisation of parallel composition modulo bisimiliarity: We argue that, under some natural assumptions, the addition of a single auxiliary binary operator to CCS does not yield a finite axiomatisation of bisimilarity. Then we delineate the boundary between finite and non-finite axiomatisability of the congruences in van Glabbeek's linear time-branching time spectrum over CCS. Finally, we present a novel result to the effect that rooted weak bisimilarity has no finite complete axiomatisation over CCS.


page 1

page 2

page 3

page 4


On the Parallel Composition for True Concurrency

For insight into the parallel composition for true concurrency, we recal...

Are Two Binary Operators Necessary to Finitely Axiomatise Parallel Composition?

Bergstra and Klop have shown that bisimilarity has a finite equational a...

On the Axiomatisation of Branching Bisimulation Congruence over CCS

In this paper we investigate the equational theory of (the restriction, ...

On the Axiomatisability of Parallel Composition

This paper studies the existence of finite equational axiomatisations of...

Fast Left Kan Extensions Using The Chase

We show how computation of left Kan extensions can be reduced to computa...

PaSe: An Extensible and Inspectable DSL for Micro-Animations

This paper presents PaSe, an extensible and inspectable DSL embedded in ...

Parallel Composition of Weighted Finite-State Transducers

Finite-state transducers (FSTs) are frequently used in speech recognitio...