Deducing Local Rules for Solving Global Tasks with Random Boolean Networks

TL;DR

This paper introduces an analytical method to determine local rules in random Boolean networks that efficiently solve global tasks like density classification and synchronization, outperforming traditional cellular automata and small-world networks.

Contribution

The authors develop a novel analytical approach to find local rules in RBNs for global tasks, demonstrating superior performance and flexibility compared to existing models.

Findings

RBNs outperform cellular automata in global task efficiency

RBNs are more effective than small-world topologies for density classification

The approach allows networks to rewire dynamically without losing performance

Abstract

It has been shown that uniform as well as non-uniform cellular automata (CA) can be evolved to perform certain computational tasks. Random Boolean networks are a generalization of two-state cellular automata, where the interconnection topology and the cell's rules are specified at random. Here we present a novel analytical approach to find the local rules of random Boolean networks (RBNs) to solve the global density classification and the synchronization task from any initial configuration. We quantitatively and qualitatively compare our results with previously published work on cellular automata and show that randomly interconnected automata are computationally more efficient in solving these two global tasks. Our approach also provides convergence and quality estimates and allows the networks to be randomly rewired during operation, without affecting the global performance. Finally, we show that RBNs outperform small-world topologies on the density classification task and that they perform equally well on the synchronization task. Our novel approach and the results may have applications in designing robust complex networks and locally interacting distributed computing systems for solving global tasks.