The Number of Fixed Points of AND-OR Networks with Chain Topology

TL;DR

This paper derives formulas to compute the number of fixed points in AND-OR Boolean networks with chain topologies, enhancing understanding of their stability and behavior.

Contribution

It provides closed and recursive formulas for fixed points in chain-topology AND-OR networks, advancing analytical tools for these networks.

Findings

Closed formulas for subclasses of networks

Recursive formulas for general cases

Effective computation methods for fixed points

Abstract

AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We find closed formulas for subclasses of these networks and recursive formulas in the general case. Our results allow for an effective computation of the number of fixed points in the case that the topology of the Boolean network is an open chain (finite or infinite) or a closed chain.