We have introduced and extended the notion of swarm automaton to analyze the computability using swarm movement represented by multiset rewriting. The two transitions, parallel and sequential, are considered to transform a configuration of multisets at each step in the swarm automaton. In this paper, we focus on the number of agents composing each configuration and analyze the computing power of swarm automaton. From the result of swarm automaton without position information, no swarm automaton has a universal computing power even though we can use infinitely many agents both in parallel rewriting and in sequential rewriting. On the other hand, when we add the information of position for each agent, the swarm automaton has universal computability. We need just four agents in a configuration to simulate any Turing machine.

我们引入并扩展了群体自动机的概念，以分析使用由多集重写表示的群体运动的可计算性。这两个转换，并行和顺序，被认为是在群体自动机的每一步转换多重集的配置。在本文中，我们关注组成每个配置的代理数量，并分析群体自动机的计算能力。从没有位置信息的群体自动机的结果来看，即使我们可以在并行重写和顺序重写中使用无限多个代理，也没有群体自动机具有通用的计算能力。另一方面，当我们为每个代理添加位置信息时，群体自动机具有通用可计算性。我们只需要一个配置中的四个代理来模拟任何图灵机。