2026/03/19 by P. Balbi, Pedro Paulo Balbi, Kévin Perrot +2 · 1 voice
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Automaton #Benchmark (surveying) #Cellular Automata and Applications #Context (archaeology) #DNA and Biological Computing #Focus (optics) #Homogeneous #Majority rule #Opinion Dynamics and Social Influence #Simple (philosophy) #cs.DC #cs.DM
paper · pdf · doi:10.48550/arxiv.2603.19472
openalex publication_date 2026/03/19 · arxiv published 2026/03/19 · arxiv updated 2026/03/19 · openalex created_date 2026/03/24 · openalex updated_date 2026/07/28
The global majority problem, often referred to as the Density Classification Task, is a classical benchmark in the context of probing the computational capabilities of automata networks. It poses the simple yet challenging problem of determining, by totally local means, whether an arbitrary initial configuration of binary states can evolve to a final, homogeneous global configuration that reflects the initial global majority. Although it is known that in the specific case of cellular automata with periodic boundaries no rule is able to solve the problem, in other formulations solutions are known and, in others, the problem is still open. Aligned with the latter, here we explore the possibility of solving the problem with automata networks, operating only with the local majority rule, with a focus on identifying non-trivial cases where it can be solved and explaining why they do so.