# The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)

## TL;DR

This paper develops a geometry of interaction model using multiple tokens to accurately represent concurrent computation in multiport interaction combinators, bridging graph theory and process algebra.

## Contribution

It introduces a novel token machine model with multiple tokens for concurrent computation, proving its soundness and adequacy for Mazza's multiport interaction nets.

## Key findings

- Model accurately captures concurrent computation.
- Proves soundness via simulation between token machines.
- Establishes adequacy through convergence analysis.

## Abstract

We introduce a geometry of interaction model for Mazza's multiport interaction combinators, a graph-theoretic formalism which is able to faithfully capture concurrent computation as embodied by process algebras like the $\pi$-calculus. The introduced model is based on token machines in which not one but multiple tokens are allowed to traverse the underlying net at the same time. We prove soundness and adequacy of the introduced model. The former is proved as a simulation result between the token machines one obtains along any reduction sequence. The latter is obtained by a fine analysis of convergence, both in nets and in token machines.