Majority Boolean networks classifying density: structural characterization and complexity
Discrete Mathematics
2026-02-17 v1
Abstract
Given a set of entities each holding a Boolean state, the Density Classification Task (DCT) asks them to converge to the most represented state. Given a directed graph of entities where each node synchronously updates to the local majority among its in-neighbors, we characterize in terms of three forbidden patterns when it solves DCT, and show that discovering these patterns is complete for NP and PSPACE.
Keywords
Cite
@article{arxiv.2602.13511,
title = {Majority Boolean networks classifying density: structural characterization and complexity},
author = {Kévin Perrot and Marius Rolland},
journal= {arXiv preprint arXiv:2602.13511},
year = {2026}
}