A framework for (de)composing with Boolean automata networks

TL;DR

This paper introduces a formal framework for decomposing and composing Boolean automata networks using modules and wirings, enabling better understanding and simulation of complex BAN systems.

Contribution

It develops a complete formalism for BAN (de)composition through modules and wirings, and demonstrates their use in proving simulation results among BANs.

Findings

Modules and wirings form a complete formalism for BAN composition.

The framework allows for proving simulation relations between different BANs.

The approach generalizes the analysis and design of Boolean automata networks.

Abstract

Boolean automata networks (BANs) are a generalisation of Boolean cellular automata. In such, any theorem describing the way BANs compute information is a strong tool that can be applied to a wide range of models of computation. In this paper we explore a way of working with BANs which involves adding external inputs to the base model (via modules), and more importantly, a way to link networks together using the above mentioned inputs (via wirings). Our aim is to develop a powerful formalism for BAN (de)composition. We formulate two results: the first one shows that our modules/wirings definition is complete, the second one uses modules/wirings to prove simulation results amongst BANs.