A weighted pair graph representation for reconstructibility of Boolean control networks

TL;DR

This paper introduces weighted pair graphs (WPGs) to represent a generalized reconstructibility concept for Boolean control networks, providing an efficient algorithm and simpler conditions for determining reconstructibility.

Contribution

It proposes WPGs as a novel representation for reconstructibility in BCNs and develops an effective algorithm based on automata theory, simplifying previous conditions.

Findings

Reconstructibility is characterized by the absence of cycles in the WPG.

Non-reconstructibility corresponds to the presence of a complete subgraph in the WPG.

The new conditions are easier to verify than previous criteria.

Abstract

A new concept of weighted pair graphs (WPGs) is proposed to represent a new reconstructibility definition for Boolean control networks (BCNs), which is a generalization of the reconstructibility definition given in [Fornasini & Valcher, TAC2013, Def. 4]. Based on the WPG representation, an effective algorithm for determining the new reconstructibility notion for BCNs is designed with the help of the theories of finite automata and formal languages. We prove that a BCN is not reconstructible iff its WPG has a complete subgraph. Besides, we prove that a BCN is reconstructible in the sense of [Fornasini & Valcher, TAC2013, Def. 4] iff its WPG has no cycles, which is simpler to be checked than the condition in [Fornasini & Valcher, TAC2013, Thm. 4].