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Computational Power of Symport/Antiport: History, Advances, and Open Problems

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Membrane Computing (WMC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3850))

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Abstract

We first give a historical overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters. We consider the number of membranes (cells in tissue P systems), the weight of the rules, and the number of objects. Then we establish our newest results: P systems with only one membrane, symport rules of weight three, and with only seven additional objects remaining in the skin membrane at the end of a halting computation are computationally complete; P systems with minimal cooperation, i.e., P systems with symport/antiport rules of size one and P systems with symport rules of weight two, are computationally complete with only two membranes with only three and six, respectively, superfluous objects remaining in the output membrane at the end of a halting computation.

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Author information

Authors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Pl. Imperial Tàrraco 1, 43005, Tarragona, Spain

    Artiom Alhazov

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

    Artiom Alhazov & Yurii Rogozhin

  3. Faculty of Informatics, Vienna University of Technology, Favoritenstr. 9–11, A–1040, Vienna, Austria

    Rudolf Freund

Authors
  1. Artiom Alhazov
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  2. Rudolf Freund
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  3. Yurii Rogozhin
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Editor information

Editors and Affiliations

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

    Rudolf Freund

  2. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucureşti, Romania

    Gheorghe Păun

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  4. Turku Centre for Computer Science (TUCS), Leminkäisenkatu 14, 20520, Turku, Finland

    Arto Salomaa

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© 2006 Springer-Verlag Berlin Heidelberg

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Alhazov, A., Freund, R., Rogozhin, Y. (2006). Computational Power of Symport/Antiport: History, Advances, and Open Problems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2005. Lecture Notes in Computer Science, vol 3850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603047_1

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  • DOI: https://doi.org/10.1007/11603047_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30948-2

  • Online ISBN: 978-3-540-32340-2

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