Majority Boolean networks classifying density: structural characterization and complexity

Kévin Perrot; Marius Rolland

Home/Archive/arXiv

arXiv · 2602.13511

Majority Boolean networks classifying density: structural characterization and complexity

Kévin Perrot·Marius Rolland

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.DM

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Kévin Perrot, Marius Rolland. 2026-02-13. Majority Boolean networks classifying density: structural characterization and complexity. https://arxiv.org/abs/2602.13511

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Quaternary Legendre Pair of Length 64

We construct an explicit quaternary Legendre pair of length $64$. To the best of our knowledge, this is the first reported construction at this length.

cs.DM↗

arXiv2026

Factorisability of Low Dimensional Non-Negative Integer Matrices

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

cs.DM↗

arXiv2026

The parameterised complexity of generalised temporal domination on temporal graphs with modular structure

Inspired by the static problem $(α,β)$-Dominating Set, we propose a general temporal domination problem, called $(α,β)$-Temporal Dominating Set ($(α,β)$-TDS). We show that this problem encompasses Temporal Dominating Set, and additionally provides first temporal extensions of problems such as $k$-Dominating Set and $α$-Dominating Set. In this paper, we study the parameterised complexity of $(α,β)$-TDS with respect to temporal neighbourhood diversity (TND), temporal modular-width (TMW), and temporal cliquewidth (TCW). We obtain fixed parameter tractability results for all values of $α$ and $β$ with respect to TND; W[1]-hardness with respect to TMW and TCW whenever $β$ is in the problem input, or whenever $α\in (0,1)$ and $β$ is a fixed constant; and para-NP-hardness with respect to TCW when $α= 0$ and $β= 1$, or $α= 1$ and $β= 0$.

cs.DM↗