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Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes

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Membrane Computing (WMC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5391))

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Abstract

Membrane computing is a formal framework of distributed parallel multiset processing. Due to massive parallelism and exponential space some intractable computational problems can be solved by P systems with active membranes in a polynomial number of steps. In this paper we generalize this approach from decisional problems to the computational ones, by providing a solution of a #P-complete problem, namely to compute the permanent of a binary matrix. The implication of this result to the PP complexity class is discussed and compared to known results about NP ∪ co −  NP.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei 5, MD-2028, Chişinău, Moldova

    Artiom Alhazov, Liudmila Burtseva, Svetlana Cojocaru & Yurii Rogozhin

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

    Yurii Rogozhin

Authors
  1. Artiom Alhazov
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  2. Liudmila Burtseva
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  3. Svetlana Cojocaru
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  4. Yurii Rogozhin
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Editor information

Editors and Affiliations

  1. School of Mathematical and Computer Science, Heriot-Watt University, EH14 8AS, Edinburgh, UK

    David Wolfe Corne

  2. School of Mathematical and Computer Science, Heriot-Watt University, EH14 4AS, Edinburgh, UK

    Pierluigi Frisco

  3. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucharest, Romania

    Gheorghe Păun

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

    Grzegorz Rozenberg

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

    Arto Salomaa

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Alhazov, A., Burtseva, L., Cojocaru, S., Rogozhin, Y. (2009). Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes. In: Corne, D.W., Frisco, P., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2008. Lecture Notes in Computer Science, vol 5391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95885-7_8

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  • DOI: https://doi.org/10.1007/978-3-540-95885-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95884-0

  • Online ISBN: 978-3-540-95885-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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