A Graph-Based Tool to Embed the {\pi}-Calculus into a Computational DPO Framework

TL;DR

This paper introduces EpiM, a graph-based tool that encodes { ext{pi}}-calculus processes as attributed graphs within a DPO framework, enabling efficient exploration of process dynamics and reduction spaces.

Contribution

It extends a DPO graph transformation framework to model { ext{pi}}-calculus, providing a generic, efficient tool for analyzing process calculi using graph rewriting techniques.

Findings

EpiM successfully encodes { ext{pi}}-calculus processes as typed attributed graphs.

The tool efficiently computes process reduction spaces using graph isomorphism checks.

EpiM is available as an accessible online Python tool.

Abstract

Graph transformation approaches have been successfully used to analyse and design chemical and biological systems. Here we build on top of a DPO framework, in which molecules are modelled as typed attributed graphs and chemical reactions are modelled as graph transformations. Edges and vertexes can be labelled with first-order terms, which can be used to encode, e.g., steric information of molecules. While targeted to chemical settings, the computational framework is intended to be very generic and applicable to the exploration of arbitrary spaces derived via iterative application of rewrite rules, such as process calculi like Milner's {\pi}-calculus. To illustrate the generality of the framework, we introduce EpiM: a tool for computing execution spaces of {\pi}-calculus processes. EpiM encodes {\pi}-calculus processes as typed attributed graphs and then exploits the existing DPO framework to compute their dynamics in the form of graphs where nodes are {\pi}-calculus processes and edges are reduction steps. EpiM takes advantage of the graph-based representation and facilities offered by the framework, like efficient isomorphism checking to prune the space without resorting to explicit structural equivalences. EpiM is available as an online Python-based tool.