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On a Păun’s Conjecture in Membrane Systems

  • Conference paper
Bio-inspired Modeling of Cognitive Tasks (IWINAC 2007)

Abstract

We study a Păun’s conjecture concerning the unsolvability of NP–complete problems by polarizationless P systems with active membranes in the usual framework, without cooperation, without priorities, without changing labels, using evolution, communication, dissolution and division rules, and working in maximal parallel manner. We also analyse a version of this conjecture where we consider polarizationless P systems working in the minimally parallel manner.

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References

  1. Alhazov, A., Freund, R.: On the efficiency of P systems with active membranes and two polarizations. In: Mauri, G., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 146–160. Springer, Heidelberg (2005)

    Google Scholar 

  2. Alhazov, A., Pérez–Jiménez, M.J.: Uniform solution to QSAT using polarizationless active membranes. In: Gutiérrez, M.A., Păun, G., Riscos, A., Romero, F.J. (eds.) Proceedings of the Fourth Brainstorming Week on Membrane Computing, vol. I, pp. 29–40. Fénix, Sevilla (2006)

    Google Scholar 

  3. Ciobanu, G., Pan, L., Păun, G., Pérez-Jiménez, M.J.: P systems with minimal parallelism. Theoretical Computer Sci., to appear

    Google Scholar 

  4. Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J.: On the power of dissolution in P systems with active membranes. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 224–240. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J., Romero–Jiménez, A.: Characterizing tractability by cell-like membrane systems. In: Subramanian, K.G., Rangarajan, K., Mukund, M. (eds.) Formal models, languages and applications. Series in Machine Perception and Artificial Intelligence, vol. 66, pp. 137–154. World Scientific, Singapore (2006)

    Google Scholar 

  6. Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A fast P system for finding a balanced 2-partition. Soft Computing 9(9), 673–678 (2005)

    Article  MATH  Google Scholar 

  7. Krishna, S.N., Rama, R.: A variant of P systems with active membranes: Solving NP–complete problems. Romanian Journal of Information Science and Technology 2(4), 357–367 (1999)

    Google Scholar 

  8. Obtulowicz, A.: Deterministic P systems for solving SAT problem. Romanian Journal of Information Science and Technology 4(1-2), 551–558 (2001)

    MathSciNet  Google Scholar 

  9. Mauri, G., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G., Salomaa, A. (eds.): WMC 2004. LNCS, vol. 3365. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  10. Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1995)

    Google Scholar 

  11. Păun, G.: P systems with active membranes: Attacking NP–complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)

    MathSciNet  MATH  Google Scholar 

  12. Păun, G.: Computing with membranes: Attacking NP–complete problems. In: Antoniou, I., Calude, C., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 94–115. Springer, London (2000)

    Google Scholar 

  13. Păun, G.: Further twenty six open problems in membrane computing. In: Gutiérrez, M.A., Riscos, A., Romero, F.J., Sburlan, D. (eds.) Proceedings of the Third Brainstorming Week on Membrane Computing, pp. 249–262. Fénix, Sevilla (2005)

    Google Scholar 

  14. Pérez-Jímenez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: The P versus NP problem through cellular computing with membranes. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 338–352. Springer, Heidelberg (2003)

    Google Scholar 

  15. Pérez-Jiménez, M.J., Riscos-Núñez, A.: Solving the Subset-Sum problem by active membranes. New Generation Computing 23(4), 367–384 (2005)

    Google Scholar 

  16. Pérez-Jímenez, M.J., Riscos-Núñez, A.: A Linear-Time Solution to the Knapsack Problem Using P Systems with Active Membranes. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 250–268. Springer, Heidelberg (2004)

    Google Scholar 

  17. Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: A polynomial complexity class in P systems using membrane division. In: Csuhaj-Varjú, E., Kintala, C., Wotschke, D., Vaszil, G. (eds.) Proceedings of the 5th Workshop on Descriptional Complexity of Formal Systems, DCFS 2003, Computer and Automation Research Institute of the Hungarian Academy of Sciences, Budapest, pp. 284–294 (2003)

    Google Scholar 

  18. Pérez Jiménez, M.J., Romero Campero, F.J.: Attacking the Common Algorithmic Problem by Recognizer P Systems. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 304–315. Springer, Heidelberg (2005)

    Google Scholar 

  19. Sosik, P.: The computational power of cell division. Natural Computing 2(3), 287–298 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zandron, C., Ferretti, C., Mauri, G.: Solving NP–complete problems using P systems with active membranes. In: Antoniou, I., Calude, C., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 289–301. Springer, Berlin (2000)

    Google Scholar 

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José Mira José R. Álvarez

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Mauri, G., Pérez-Jiménez, M.J., Zandron, C. (2007). On a Păun’s Conjecture in Membrane Systems. In: Mira, J., Álvarez, J.R. (eds) Bio-inspired Modeling of Cognitive Tasks. IWINAC 2007. Lecture Notes in Computer Science, vol 4527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73053-8_18

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  • DOI: https://doi.org/10.1007/978-3-540-73053-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73052-1

  • Online ISBN: 978-3-540-73053-8

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