A Formal Approach to Open Multiparty Interactions

TL;DR

This paper introduces Core Network Algebra (CNA), a process calculus for modeling open, multiparty interactions without fixed process counts, extending CCS with a novel semantics that supports congruence and substitution.

Contribution

It proposes CNA, a new process algebra for open multiparty interactions, with a unique semantics ensuring congruence and substitution invariance, unlike traditional bisimilarity.

Findings

CNA effectively models open multiparty interactions.

The semantics is a congruence for all CNA operators.

Application to software defined networks demonstrates practicality.

Abstract

We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus on the theory of a core version of a process calculus, without message passing, called Core Network Algebra (CNA). In CNA communication actions are given not in terms of channels but in terms of chains of links that record the source and the target ends of each hop of interactions. The operational semantics of our calculus mildly extends the one of CCS. The abstract semantics is given in the style of bisimulation but requires some ingenuity. Remarkably, the abstract semantics is a congruence for all operators of CNA and also with respect to substitutions, which is not the case for strong bisimilarity in CCS. As a motivating and running example, we illustrate the model of a simple software defined network infrastructure.