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On the Hierarchy of Swarm-automaton for the Number of Agents

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Abstract

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.

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Acknowledgements

We would like to thank the anonymous reviewers for their constructive comments. Especially, we express our sincere thanks to Dr. Shinnosuke Seki for the idea of the proof of Lemma 19.

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  1. International College of Arts and Sciences, Fukuoka Women’s University, 1-1-1 Kasumigaoka, Higashi-ku, Fukuoka, 813-8529, Japan

    Kaoru Fujioka

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  1. Kaoru Fujioka
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Correspondence to Kaoru Fujioka.

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Fujioka, K. On the Hierarchy of Swarm-automaton for the Number of Agents. Theory Comput Syst 67, 714–731 (2023). https://doi.org/10.1007/s00224-023-10117-z

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