Decomposition with respect to outputs for Boolean control networks

TL;DR

This paper presents algebraic and graphical conditions for decomposing Boolean control networks with respect to outputs, along with an efficient method to implement the decomposition and validation through examples.

Contribution

It introduces a novel algebraic and graphical framework for output-based decomposition of BCNs and proposes a computationally efficient realization method.

Findings

Derived algebraic conditions for BCN decomposition

Established a necessary and sufficient graphical condition

Validated the method with practical examples

Abstract

This paper investigates the problem of decomposition with respect to outputs for Boolean control networks (BCNs). First, with the linear expression of BCNs and the matrix semi-tensor product, some algebraic equivalent conditions for the decomposition are obtained. Second, a necessary and sufficient graphical condition for the decomposition with respect to outputs is given. Third, an effective method is proposed to reduce the computational burden in the realization of the decomposition. Finally, some examples are addressed to validate the effectiveness of the proposed method.