Computational Complexity Aspects in Membrane Computing

  • Giancarlo Mauri
  • Alberto Leporati
  • Antonio E. Porreca
  • Claudio Zandron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)

Abstract

Within the framework of membrane systems, distributed parallel computing models inspired by the functioning of the living cell, various computational complexity classes have been defined, which can be compared against the computational complexity classes defined for Turing machines. Here some issues and results concerning computational complexity of membrane systems are discussed. In particular, we focus our attention on the comparison among complexity classes for membrane systems with active membranes (where new membranes can be created by division of membranes which exist in the system in a given moment) and the classes PSPACE, EXP, and EXPSPACE.

Keywords

Membrane systems Computational complexity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alhazov, A., Martín-Vide, C., Pan, L.: Solving a PSPACE-complete problem by P systems with restricted active membranes. Fundamenta Informaticae 58(2), 67–77 (2003)MathSciNetGoogle Scholar
  2. 2.
    Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J.: P systems with active membranes, without polarizations and without dissolution: a characterization of P. In: Calude, C.S., Dinneen, M.J., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 105–116. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Krishna, S.N., Rama, R.: A variant of P systems with active membranes: Solving NP-complete problems. Romanian J. of Information Science and Technology 2(4), 357–367 (1999)Google Scholar
  4. 4.
    Leporati, A., Zandron, C., Ferretti, C., Mauri, G.: On the Computational Power of Spiking Neural P Systems. Intern. J. of Unconventional Computing 5(5), 459–473 (2009)Google Scholar
  5. 5.
    Leporati, A., Mauri, G., Zandron, C., Păun, G., Pérez-Jiménez, M.J.: Uniform Solutions to SAT and Subset Sum by Spiking Neural P Systems. Natural Computing 8(4), 681–702 (2009)MATHCrossRefGoogle Scholar
  6. 6.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1993)Google Scholar
  7. 7.
    Păun, G.: Computing with membranes. J. of Computer and System Sciences 61(1), 108–143 (2000)MATHCrossRefGoogle Scholar
  8. 8.
    Păun, G.: P systems with active membranes: attacking NP complete problems. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 94–115. Springer, London (2000)Google Scholar
  9. 9.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  10. 10.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2009)Google Scholar
  11. 11.
    Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Complexity Classes in Cellular Computing with Membranes. Natural Computing 2(3), 265–285 (2003)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    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 (2004)Google Scholar
  13. 13.
    Porreca, A.E., Mauri, G., Zandron, C.: Complexity classes for membrane systems. RAIRO Theoretical Informatics and Applications 40(2), 141–162 (2006)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Porreca, A.E., Mauri, G., Zandron, C.: Non-confluence in divisionless P systems with active membranes. Theoretical Computer Science 411(6), 878–887 (2010)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sosík, P.: The computational power of cell division in P systems: Beating down parallel computers? Natural Computing 2(3), 287–298 (2003)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sosík, P., Rodríguez-Patón, A.: Membrane computing and complexity theory: a characterization of PSPACE. Journal of Computer and System Sciences 73(1), 137–152 (2007)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Zandron, C., Ferretti, C., Mauri, G.: Solving NP-complete problems using P systems with active membranes. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 289–301. Springer, London (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Giancarlo Mauri
    • 1
  • Alberto Leporati
    • 1
  • Antonio E. Porreca
    • 1
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations