A process algebra for the Span(Graph) model of concurrency

TL;DR

This paper introduces TCP, a process algebra aligned with the Span(RGraph) automata model, capturing concurrency, asynchrony, and communication through interfaces with a compositional semantics.

Contribution

It defines TCP, a novel process algebra that closely models concurrency using Span(RGraph), integrating interfaces, asynchronous actions, and anonymous communication.

Findings

TCP accurately models concurrent processes with fixed interfaces.

The algebra incorporates silent actions for asynchrony.

It provides a compositional semantics based on Span(RGraph).

Abstract

In this note we define a process algebra TCP (Truly Concurrent Processes) which corresponds closely with the automata model of concurrency based on Span(RGraph), the category of spans of reflexive graphs. In TCP, each process has a fixed set of interfaces. Actions are allowed to occur simultaneously on all the interfaces of a process. Asynchrony is modelled by the use of silent actions. Communication is anonymous: communication between two processes P and Q is described by an operation which connects some of the ports of P to some of the ports of Q; and a process can only communicate with other processes via its interfaces. The model is naturally equipped with a compositional semantics in terms of the operations in Span(RGraph) introduced in [5], and developed in [6, 7, 10].