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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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References

  1. Csuhaj-Varjú, E.: P automata. WMC 2009. Lect. Notes Comput. Sci 3365, 69–84 (2004)

    Google Scholar 

  2. Fujioka, K.: Swarm-based multiset rewriting computing models. UCNC 2019. Lect. Notes Comput. Sci 11493, 79–93 (2019)

    Article  MATH  Google Scholar 

  3. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to automata theory, languages and computation pearson Addison-Wesley (2007)

  4. Ibarra, O.H.: On membrane hierarchy in p systems. Theor. Comput. Sci. 334(1), 115–129 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lindenmayer, A.: Mathematical models for cellular interactions in development i. filaments with one-sided inputs. J. Theor. Biol. 18(3), 280–299 (1968). https://doi.org/10.1016/0022-5193(68)90079-9

    Article  Google Scholar 

  6. von Mammen, S., Jacob, C.: Evolutionary swarm design of architectural idea models. In: Proceedings of the 10th annual conference on genetic and evolutionary computation, GECCO ’08, pp. 143-150, ACM, New York, NY, USA (2008)

  7. von Mammen, S., Phillips, D., Davison, T., Jacob, C.: A graph-based developmental swarm representation and algorithm. In: Swarm Intelligence pp. 1–12. Springer Berlin Heidelberg, Berlin, Heidelberg (2010)

  8. Nielsen, M., Rozenberg, G., Salomaa, A., Skyum, S.: Nonterminals, homomorphisms and codings in different variations of 0L-systems. Acta Inform. 3(4), 357–364 (1974)

    Article  MATH  Google Scholar 

  9. Paun, G., Rozenberg, G., Salomaa, A.: The oxford handbook of membrane computing. Oxford University Press, Inc., New York, NY USA (2010)

  10. Reynolds, C.W.: Flocks, herds and schools: a distributed behavioral model. SIGGRAPH Comput. Graph. 21(4), 25–34 (1987)

    Article  Google Scholar 

  11. Rozenberg, G., Salomaa, A.: (eds.): Handbook of Formal Languages. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

Download references

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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