An Approach to Computational Complexity in Membrane Computing

  • Mario J. Pérez-Jiménez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3365)

Abstract

In this paper we present a theory of computational complexity in the framework of membrane computing. Polynomial complexity classes in recognizer membrane systems and capturing the classical deterministic and non-deterministic modes of computation, are introduced. In this context, a characterization of the relation P = NP is described.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alhazov, A., Freund, R., Păun, G.: P systems with active membranes and two polarizations. In: Păun, G., Riscos, A., Romero, A., Sancho, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, pp. 20–35 (2004)Google Scholar
  2. 2.
    Alhazov, A., Ishdorj, T.-O.: Membrane operations in P systems with active membranes. In: Păun, G., Riscos, A., Romero, A., Sancho, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, pp. 37–52 (2004)Google Scholar
  3. 3.
    Alhazov, A., Martín–Vide, C., Pan, L.: Solving graph problems by P systems with restricted elementary active membranes. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 1–22. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Alhazov, A., Pan, L., Păun, G.: Trading polarizations for labels in P systems with active membranes. Acta Informatica (to appear)Google Scholar
  5. 5.
    Castellanos, J., Păun, G., Rodríguez–Patón, A.: P systems with worm–objects. In: IEEE 7th International Conference on String Processing and Information Retrieval, SPIRE 2000, La Coruña, Spain, pp. 64–74 (2000)Google Scholar
  6. 6.
    Cordón–Franco, A., Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Sancho–Caparrini, F.: Implementing in Prolog an effective cellular solution for the Knapsack problem. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 140–152. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Czeiler, E.: Self–activating P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 234–246. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)MATHGoogle Scholar
  9. 9.
    Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A.: A fast P system for finding a balanced 2-partition. Soft Computing (in press)Google Scholar
  10. 10.
    Head, T., Yamamura, M., Gal, S.: Aqueous computing: writing on molecules. In: Proceedings of the Congress on Evolutionary Computation 1999, pp. 1006–1010. IEEE Service Center, Piscataway (1999)Google Scholar
  11. 11.
    Ito, M., Martín–Vide, C., Păun, G.: Characterization of Parikh sets of ET0L languages in terms of P systems. In: Ito, M., Păun, G., Yu, S. (eds.) Words, Semigroups, and Transducers, pp. 239–254. World Scientific, Singapore (2001)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Krishna, S.N., Rama, R.: P systems with replicated rewriting. Journal of Automata, Languages and Combinatorics 6(1), 345–350 (2001)MATHMathSciNetGoogle Scholar
  14. 14.
    Krishna, S.N., Rama, R.: Breaking DES using P systems. Theoretical Computer Science 299(1-3), 495–508 (2003)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Madhu, M., Kristhivasan, K.: P systems with membrane creation: Universality and efficiency. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 276–287. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Obtulowicz, A.: Deterministic P systems for solving SAT problem. Romanian Journal of Information Science and Technology 4(1–2), 551–558 (2001)MathSciNetGoogle Scholar
  17. 17.
    Obtułowicz, A.: On P Systems with Active Membranes Solving the Integer Factorization Problem in a Polynomial Time. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 267–285. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Obtulowicz, A.: Note on some recursively family of P systems with active membranes (2004) (Submitted)Google Scholar
  19. 19.
    Pan, L., Alhazov, A., Ishdorj, T.-O.: Further remarks on P systems with active membranes, separation, merging, and release rules. In: Păun, G., Riscos, A., Romero, A., Sancho, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, pp. 316–324 (2004)Google Scholar
  20. 20.
    Pan, L., Ishdorj, T.-O.: P systems with active membranes and separation rules. Journal of Universal Computer Science 10(5), 630–649 (2004)MathSciNetGoogle Scholar
  21. 21.
    Pan, L., Martín–Vide, C.: C. Solving multiset 0–1 knapsack problem by P systems with input and active membranes. In: Păun, G., Riscos, A., Romero, A., Sancho, F. (eds.) Proceedings of the Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, pp. 342–353 (2004)Google Scholar
  22. 22.
    Păun, A.: On P systems with membrane division. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 187–201. Springer, London (2000)Google Scholar
  23. 23.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000); and Turku Center for Computer Science-TUCS Report Nr. 208 (1998)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Păun, G.: Computing with membranes: Attacking NP–complete problems. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 94–115 (2000)Google Scholar
  25. 25.
    Păun, G.: P systems with active membranes: Attacking NP–complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)MATHMathSciNetGoogle Scholar
  26. 26.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  27. 27.
    Păun, G., Pérez–Jiménez, M.J., Riscos–Núñez, A.: P systems with tables of rules. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds.) Theory Is Forever. LNCS, vol. 3113, pp. 235–249. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Păun, G., Rozenberg, G.: A guide to membrane computing. Theoretical Computer Science 287, 73–100 (2002)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Păun, G., Suzuki, Y., Tanaka, H., Yokomori, T.: On the power of membrane division in P systems. Theoretical Computer Science 324(1), 61–85 (2004)MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Pérez–Jiménez, M.J., Riscos–Núñez, A.: Solving the Subset-Sum problem by P systems with active membranes. New Generation Computing (in press)Google Scholar
  31. 31.
    Pérez–Jiménez, M.J., Riscos–Núñez, A.: A linear time solution to the Knapsack problem using 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)CrossRefGoogle Scholar
  32. 32.
    Pérez–Jiménez, M.J., Romero-Campero, F.J.: Trading polarizations for bi-stable catalysts in P systems with active membranes. In this volumeGoogle Scholar
  33. 33.
    Pérez–Jiménez, M.J., Romero-Campero, F.J.: An efficient family of P systems for packing items into bins. Journal of Universal Computer Science 10(5), 650–670 (2004)MathSciNetGoogle Scholar
  34. 34.
    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, p. 27. Springer, Heidelberg (2005)Google Scholar
  35. 35.
    Pérez–Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Teoría de la Complejidad en Modelos de Computación con Membranas. Ed. Kronos, Sevilla (2002)Google Scholar
  36. 36.
    Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: Complexity classes in models of cellular computing with membranes. Natural Computing 2(3), 265–285 (2003)MATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: Solving VALIDITY problem by active membranes with input. In: Cavaliere, M., Martín-Vide, C., Păun, G. (eds.) Proceedings of the Brainstorming Week on Membrane Computing, Report GRLMC 26/03, pp. 279–290 (2003)Google Scholar
  38. 38.
    Pérez–Jiménez, 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)CrossRefGoogle Scholar
  39. 39.
    Riscos-Núñez, A.: Programación celular: Resolución eficiente de problemas numéricos NP–completos. PhD. Thesis, University of Seville, Spain (2004)Google Scholar
  40. 40.
    Romero-Jiménez, A.: Complexity and Universality in Cellular Computing Models, PhD. Thesis, University of Seville, Spain (2003)Google Scholar
  41. 41.
    Romero-Jiménez, A., Pérez–Jiménez, M.J.: Simulating Turing machines by P systems with external output. Fundamenta Informaticae 49(1-3), 273–287 (2002)MATHMathSciNetGoogle Scholar
  42. 42.
    Sosik, P.: The computational power of cell division. Natural Computing 2(3), 287–298 (2003)MATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Zandron, C., Ferreti, 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, UMC 2000, pp. 289–301. Springer, Berlin (2000)Google Scholar
  44. 44.
    Zandron, C., Mauri, G., Ferreti, C.: Universality and normal forms on membrane systems. In: Freund, R., Kelemenova, A. (eds.) Proceedings International Workshop on Grammar Systems, Bad Ischl, Austria, July 2000, pp. 61–74 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mario J. Pérez-Jiménez
    • 1
  1. 1.Research Group on Natural Computing,Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

Personalised recommendations