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Workshop on Membrane Computing

WMC 2002: Membrane Computing pp 319–338Cite as

Accretive Rules in Cayley P Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2597))

Abstract

During a discussion taking place at WMC’01, G. Paun put the question of what could be computed only by moving symbols between membranes. In this paper we provide some elements of the answer, in a setting similar to tissue Psystems, where the set of membranes is organized into a finite graph or into a Cayley graph, and using a very simple propagation process characterizing accretive growth. Our main result is to characterize the final configuration as a least fixed point and to establish two series of approximations that converge to it. All the notions introduced (Cayley graph of membranes, accretive rule and iteration) have been implemented in the MGS programming language and the two approximation series can be effectively computed in Pressburger arithmetics using the omega calculator in the case of Abelian Cayley graphs.

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Author information

Authors and Affiliations

  1. LaMI, umr 8042 du CNRS, Université d’Évry - GENOPOLE, Tour Evry-2, 523 Place des Terrasses de l’Agora, 91000, Évry, France

    Giavitto Jean-Louis, Olivier Michel & Julien Cohen

Authors
  1. Giavitto Jean-Louis
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  2. Olivier Michel
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  3. Julien Cohen
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Editor information

Editors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe PĂun

  2. Leiden University, Leiden Institute of Advanced Computer Science, Niels Bohrweg 1, 2333, CA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

  4. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, 20126, Milano, Italy

    Claudio Zandron

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© 2003 Springer-Verlag Berlin Heidelberg

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Jean-Louis, G., Michel, O., Cohen, J. (2003). Accretive Rules in Cayley P Systems. In: PĂun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. WMC 2002. Lecture Notes in Computer Science, vol 2597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36490-0_21

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  • DOI: https://doi.org/10.1007/3-540-36490-0_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00611-4

  • Online ISBN: 978-3-540-36490-0

  • eBook Packages: Springer Book Archive

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