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Sequential and maximally parallel multiset rewriting: reversibility and determinism

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Abstract

We study reversibility and determinism aspects and the strong versions of these properties of sequential multiset processing systems and of maximally parallel systems, from the computability point of view. In the sequential case, syntactic criteria are established for both strong determinism and strong reversibility. In the parallel case, a criterion is established for strong determinism, whereas strong reversibility is shown to be decidable. In the sequential case, without control all four classes—deterministic, strongly deterministic, reversible, strongly reversible—are not universal, whereas in the parallel case deterministic systems are universal. When allowing inhibitors, the first and the third class become universal in both models, whereas with priorities all of them are universal. In the maximally parallel case, strongly deterministic systems with both promoters and inhibitors are universal. We also present a few more specific results and conjectures.

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Acknowledgments

Artiom Alhazov gratefully acknowledges the support of the Japan Society for the Promotion of Science and the Grant-in-Aid for Scientific Research, project \(20\cdot08364\). He also acknowledges the support by the Science and Technology Center in Ukraine, project 4032.

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Authors and Affiliations

  1. FCS, Department of Information Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Artiom Alhazov & Kenichi Morita

  2. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei 5, Chişinău, 2028, Moldova

    Artiom Alhazov

  3. Faculty of Informatics, Vienna University of Technology, Favoritenstr. 9, 1040, Vienna, Austria

    Rudolf Freund

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  1. Artiom Alhazov
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  2. Rudolf Freund
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  3. Kenichi Morita
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Correspondence to Artiom Alhazov.

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Alhazov, A., Freund, R. & Morita, K. Sequential and maximally parallel multiset rewriting: reversibility and determinism. Nat Comput 11, 95–106 (2012). https://doi.org/10.1007/s11047-011-9267-8

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  • DOI: https://doi.org/10.1007/s11047-011-9267-8

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