On Barbs and Labels in Reactive Systems

TL;DR

This paper introduces L-bisimilarity, a new behavioral equivalence for reactive systems that generalizes existing notions and can be applied to various calculi like CCS and mobile ambients.

Contribution

It proposes L-bisimilarity, an intermediate, parametric behavioral equivalence that unifies IPO, saturated bisimulations, and barbed semantics for reactive systems.

Findings

L-bisimilarity is a congruence under mild conditions.

It recasts IPO and saturated bisimulations within a unified framework.

The approach is instantiated for CCS and mobile ambients.

Abstract

Reactive systems (RSs) represent a meta-framework aimed at deriving behavioral congruences for those computational formalisms whose operational semantics is provided by reduction rules. RSs proved a flexible specification device, yet so far most of the efforts dealing with their behavioural semantics focused on idem pushouts (IPOs) and saturated (also known as dynamic) bisimulations. In this paper we introduce a novel, intermediate behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts. The equivalence is parametric with respect to a set L of RSs labels, and it is shown that under mild conditions on L it is indeed a congruence. Furthermore, L-bisimilarity can also recast the notion of barbed semantics for RSs, proposed by the same authors in a previous paper. In order to provide a suitable test-bed, we instantiate our proposal by addressing the semantics of (asynchronous) CCS and of the calculus of mobile ambients.