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P Systems with Generalized Multisets Over Totally Ordered Abelian Groups

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Book cover Membrane Computing (CMC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9504))

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Abstract

In this paper we extend the definition of a multiset by allowing elements to have multiplicities from an arbitrary totally ordered Abelian group instead of only using natural numbers. We consider P systems with such generalized multisets and give well-founded notations for the applicability of rules and for different derivation modes. These new definitions raise challenging mathematical questions and we propose several solutions yielding models sometimes having quite unexpected behavior. Another interesting application of our results is the possibility to consider complex objects and to manipulate them directly in a P system instead of their numerical encodings.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, TU Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Rudolf Freund

  2. LACL, Université Paris Est – Créteil Val de Marne, 61, av. Général de Gaulle, 94010, Créteil, France

    Sergiu Ivanov & Sergey Verlan

Authors
  1. Rudolf Freund
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  2. Sergiu Ivanov
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  3. Sergey Verlan
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Corresponding author

Correspondence to Rudolf Freund .

Editor information

Editors and Affiliations

  1. LIACS, Leiden University, Leiden, Zuid-Holland, The Netherlands

    Grzegorz Rozenberg

  2. Turku Center for Computer Science, Turku, Finland

    Arto Salomaa

  3. Universidad Politécnica de Valencia, Valencia, Spain

    José M. Sempere

  4. University of Milan-Bicocca, Milano, Italy

    Claudio Zandron

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Freund, R., Ivanov, S., Verlan, S. (2015). P Systems with Generalized Multisets Over Totally Ordered Abelian Groups. In: Rozenberg, G., Salomaa, A., Sempere, J., Zandron, C. (eds) Membrane Computing. CMC 2015. Lecture Notes in Computer Science(), vol 9504. Springer, Cham. https://doi.org/10.1007/978-3-319-28475-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-28475-0_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28474-3

  • Online ISBN: 978-3-319-28475-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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