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Solving NP-complete Problems in Polynomial Time by Using a Natural Computing Model

  • Bogdan AmanEmail author
  • Gabriel Ciobanu
Conference paper
  • 313 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 594)

Abstract

The first part of the paper is devoted to a polynomial solution of a well-known NP-complete problem (SAT problem) by using an unconventional computation model provided by P systems with active membranes (with neither polarization nor division rules). An important step of this semi-uniform solution is given by polynomial computing devices to build P systems that contain some exponential-size feature for which solving the SAT problem is easy. NP-complete problems are decision problems that can be solved in polynomial time on a non-deterministic Turing machine. Related to this step, in the second part we show how we can simulate polynomial space Turing machines by using a logarithmic space P system with active membranes, and employing a binary representation in order to encode the positions on the Turing machine tape.

Keywords

Natural computing Membrane computing Turing machines 

References

  1. 1.
    Aman, B., Ciobanu, G.: Describing the immune system using enhanced mobile membranes. Electron. Notes Theoret. Comput. Sci. 194, 5–18 (2008)CrossRefGoogle Scholar
  2. 2.
    Aman, B., Ciobanu, G.: Turing completeness using three mobile membranes. In: Calude, C.S., Costa, J.F., Dershowitz, N., Freire, E., Rozenberg, G. (eds.) UC 2009. LNCS, vol. 5715, pp. 42–55. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Aman, B., Ciobanu, G.: Mobility in Process Calculi and Natural Computing. Natural Computing Series. Springer, New York (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    Besozzi, D., Ciobanu, G.: A P system description of the Sodium-Potassium pump. In: Mauri, G., Păun, G., Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 210–223. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Bonchiş, C., Ciobanu, G., Izbaşa, C.: Encodings and arithmetic operations in membrane computing. In: Cai, J.-Y., Cooper, S.B., Li, A. (eds.) TAMC 2006. LNCS, vol. 3959, pp. 621–630. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Cavaliere, M.: Evolution-communication P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 134–145. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds.): Applications of Membrane Computing. Springer, New York (2006)Google Scholar
  8. 8.
    Krishna, S.N., Rama, R.: P systems with replicated rewriting. J. Automata Lang. Comb. 6(3), 345–350 (2001)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Leporati, A., Gutiérrez-Naranjo, M.A.: Solving subset sum by spiking neural P Systems with pre-computed resources. Fundamenta Informaticae 87(1), 61–77 (2008)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Constant-space P systems with active membranes. Fundamenta Informaticae 134(1–2), 111–128 (2014)MathSciNetGoogle Scholar
  11. 11.
    Leporati, A., Mauri, G., Porreca, A.E., Zandron, C.: A gap in the space hierarchy of P systems with active membranes. J. Automata Lang. Comb. 19(1–4), 173–184 (2014)MathSciNetGoogle Scholar
  12. 12.
    Murphy, N., Woods, D.: The computational power of membrane systems under tight uniformity conditions. Nat. Comput. 10, 613–632 (2011)CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Păun, G.: P systems with active membranes: attacking NP-complete problems. J. Automata Lang. Comb. 6, 75–90 (2001)zbMATHGoogle Scholar
  14. 14.
    Păun, G.: Further Twenty Six Open Problems in Membrane Computing. In: Gutiérrez, M.A., et al. (eds.) Third Brainstorming Week on Membrane Computing, pp. 249–262, Fénix Editora, Sevilla (2005)Google Scholar
  15. 15.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar
  16. 16.
    Pérez-Jiménez, M.J., Riscos-Núñez, A., Romero-Jiménez, A., Woods, D.: Complexity-membrane division, membrane creation. In: [15], pp. 302–336Google Scholar
  17. 17.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: Sublinear-space P systems with active membranes. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds.) CMC 2012. LNCS, vol. 7762, pp. 342–357. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Romanian Academy, Institute of Computer ScienceIaşiRomania

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