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.

翻译：全局多数问题（常称为密度分类任务）是评估自组织网络计算能力的经典基准。该问题通过完全局部的机制，判断任意初始二元状态配置能否演化为反映初始全局多态的最终同质全局配置，虽简单但极具挑战。已知在周期边界元胞自动机的特定情形下，不存在能解决该问题的规则，但在其他表述中已有解决方案，而某些情形下该问题仍未解决。本文针对后者，探索仅使用局部多数规则的自组织网络能否求解该问题，着重识别可求解的非平凡案例并解释其成功机理。