On the computational power of swarm automata using agents with position information

Based on swarm movements and computing models using multisets, a swarm automaton was introduced to construct a new computing system using swarm behavior in the computing process. In a swarm automaton, each agent changes by input and the interaction between agents, which leads to change the swarm represented by the multiset of agents. An input string is accepted by a swarm automaton depending on the conditions of the agents in the swarm. That is, an input string that leads the swarm to a specified condition is accepted. When we introduce position information for agents in a swarm automaton, the agent not only changes but also moves according to the nearby agents. In this paper, we introduce a language accepted by a swarm automaton based on the position of agents in a swarm. That is, a string is accepted when it leads to the swarm consisting of agents on the designated position. We focus on the number of agents in a swarm and consider the computing power of that swarm automaton. We show that any recursively enumerable language is accepted by a swarm automaton with only five agents using parallel transition.