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Solving the Subset-Sum problem by P systems with active membranes

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Abstract

We present the first membrance computing solution to the Subset-Sum problem using a family of deterministic P systems with active membranes. We do not use priority among rules, membrane dissolution nor cooperation; it suffices to control the electrical charges of the membranes and to introduce some counters. The number of steps of any computation is of the linear order (but it is necessary a polynomial-time of precomputed resources).

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References

  1. Cordón Franco, A., Gutiérrez Naranjo, M. A., Pérez Jiménez, M. J. and Riscos Núñez, A., “Cellular Solutions for Some Numerical NP-complete Problems: A Prolog Implementation,”Molecular Computational Models: Unconventional Approaches (Gheorghe, M. ed), Idea Group, Inc., pp. 115–149, 2005.

  2. Cordón Franco, A., Gutiérrez Naranjo, M. A., Pérez Jiménez, M. J. and Sancho Caparrini, F., “A Prolog Simulator for Deterministic P systems with Active membranes,”New Generation Computing, 22, pp. 349–363, 2004.

    Article  MATH  Google Scholar 

  3. Narayanan, K. S., “Languages of P Systems: Computability and Complexity,” Ph.D. Thesis, Indian Institute of Technology Madras.

  4. Pérez Jiménez, M. J., Romero Jiménez, A. and Sancho Caparrini, F. “Decision P Systems and theP ≠ NP Conjecture,”Lecture Notes in Computer Science, 2597, pp. 390–401, 2003.

    Google Scholar 

  5. Pérez Jiménez, M. J., Romero Jiménez, A. and Sancho Caparrini, F., “Solving Validity Problem by Active Membranes with Input,”Brainstorming Week on Membrane Computing (Cavaliere, M., Martín-Vide, C. and G. Pâun, eds.),Report GRLM 26/03, pp. 279–290, 2003.

  6. Pérez Jiménez, M. J., Romero Jiménez, A. and Sancho Caparrini, F.,Teoría de la Complejidad en Modelos de Computación Celular con Membranas (Kronos, ed.), Sevilla, 2002.

  7. Pérez Jiménez, M. J., Romero Jiménez, A. and Sancho Caparrini, F., “Complexity Classes in Cellular Computing with Membranes,”Natural Computing, 2, 3, pp. 265–285, 2004.

    Article  Google Scholar 

  8. Pérez-Jiménez, M. J., Riscos-Núñez, A., “A Linear Solution for the Knapsack Problem Using Active Membranes,”Membrane Computing (Martín-Vide, C., Mauri, G., Pâun, Gh., Rozenberg, G. and Salomaa, A. eds.),Lecture Notes in Computer Science, 2933, pp. 250–268, 2004.

  9. Pâun, Gh., “Computing with Membranes,”Journal of Computer and System Sciences, 61, 1, pp. 108–143, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  10. Pâun, Gh., “P Systems with Active Membranes: Attacking NP Complete Problems,”Journal of Automata, Languages and Combinatorics, 6, 1, pp. 75–90, 2001.

    MATH  MathSciNet  Google Scholar 

  11. Pâun, Gh.,Membrane Computing. An Introduction, Springer-Verlag, Berlin, 2002.

    MATH  Google Scholar 

  12. Zandron, C., “A Model for Molecular Computing: Membrane Systems,” Ph.D. Thesis, Università degli Studi di Milano.

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Authors and Affiliations

  1. Dpto. Ciencias de la Computación e Inteligencia Artificial E.T.S. Ingeniería Informática, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012, Sevilla, España

    Mario J. Pérez Jiménez & Agustín Riscos Núñez

Authors
  1. Mario J. Pérez Jiménez
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  2. Agustín Riscos Núñez
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Correspondence to Mario J. Pérez Jiménez.

Additional information

Mario J. Pérez Jiménez: He is a Titular Professor of Department of Computer Science and Artificial Intelligence at University of Seville, where he is the head of the Research Group on Natural Computing. He has published 8 books of Mathematics and Computation, and more than 100 scientific articles in prestigious scientific journals. He is a member of European Molecular Computing Consortium, and has been an independent expert to the evaluation of NEST (New and Emergent Science and Technology) proposals under the Sixth Framework Programme of the European Community.

Agustín Riscos Núñez: He holds a research fellowship at the Departament of Computer Science and Artificial Intelligence area in the University of Seville since november 2001. He is a member of the Research Group on Natural Computing and also of European Molecular Computing Consortium. His main interests are complexity theory, membrane computing and other areas of Natural Computing, both at the theoretical level and the level of computer simulation. In last year he has actively collaborated with other members of the Research Group to several International Conferences and publishing several papers in international journals.

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Jiménez, M.J.P., Núñez, A.R. Solving the Subset-Sum problem by P systems with active membranes. New Gener Comput 23, 339–356 (2005). https://doi.org/10.1007/BF03037637

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  • DOI: https://doi.org/10.1007/BF03037637

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