Set stabilization of Boolean control networks based on bisimulations: A dimensionality reduction approach

TL;DR

This paper introduces a bisimulation-based approach to analyze set stabilization in Boolean control networks, reducing complexity through algebraic morphisms and extending to probabilistic networks for unified analysis.

Contribution

It develops a novel verification method using bisimulation matrices for Boolean control networks and extends the framework to probabilistic networks for comprehensive analysis.

Findings

Bisimulation matrices effectively verify set stabilization.

Comparison of weak and strong bisimulation impacts system complexity.

Method validated through a practical example.

Abstract

This paper exploits bisimulation relations, generated by extracting the concept of morphisms between algebraic structures, to analyze set stabilization of Boolean control networks with lower complexity. First, for two kinds of bisimulation relations, called as weak bisimulation and strong bisimulation relations, a novel verification method is provided by constructing the bisimulation matrices. Then the comparison for set stabilization of BCNs via two kinds of bisimulation methods is presented, which involves the dimensionality of quotient systems and dependency of the control laws on the original system. Moreover, the proposed method is also applied to the analysis of probabilistic Boolean control networks to establish the unified analysis framework of bisimulations. Finally, the validity of the obtained results is verified by the practical example.