Dynamics Decomposition of Boolean Networks: An algebraic foundation

2026-07-23

AI Summary

This study addresses the challenge of modular decomposition in large-scale Boolean networks while preserving dynamic behavioral consistency. The authors propose a novel approach grounded in semiring algebraic structures, introducing semiring theory into the dynamical space of Boolean networks to construct a rigorous algebraic framework. This framework enables the systematic decomposition of global dynamics into compositions of local subnetwork dynamics. For the first time, this work establishes an algebraic foundation for modular dynamic decomposition of Boolean networks, elucidating the compositional relationship between local and global behaviors. It further provides scalable mathematical tools and theoretical support for network reduction, control, design, and reverse engineering.

Abstract

Understanding the dynamics of Boolean networks is central to problems such as network reduction, design, control, and reverse engineering. As Boolean network models continue to grow in size and complexity, it becomes increasingly important to decompose networks into modules in a manner that is compatible with their dynamics. In this paper, we show that endowing the space of possible dynamics with a semiring structure enables a systematic decomposition of the dynamics of any Boolean network in terms of the dynamics of its constituent modules. This algebraic framework provides a systematic way to analyze how local dynamical behaviors combine to produce global dynamics. Our results establish a concrete algebraic foundation for network modularity and introduce new mathematical tools for the study of complex Boolean networks, and opens the door to the application of algebraic methods to problems of network analysis, decomposition, and control.

Problem

• Boolean networks
• dynamics decomposition
• network modularity
• algebraic foundation

Innovation

• Boolean networks
• dynamics decomposition
• semiring structure
• network modularity
• algebraic framework