Advertisement

Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes

  • Artiom Alhazov
  • Liudmila Burtseva
  • Svetlana Cojocaru
  • Yurii Rogozhin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5391)

Abstract

Membrane computing is a formal framework of distributed parallel multiset processing. Due to massive parallelism and exponential space some intractable computational problems can be solved by P systems with active membranes in a polynomial number of steps. In this paper we generalize this approach from decisional problems to the computational ones, by providing a solution of a #P-complete problem, namely to compute the permanent of a binary matrix. The implication of this result to the PP complexity class is discussed and compared to known results about NP ∪ co −  NP.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alhazov, A., Pan, L., Păun, G.: Trading polarizations for labels in P systems with active membranes. Acta Informaticae 41, 111–144 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Gill, J.: Computational complexity of probabilistic Turing machines. SIAM Journal on Computing 6, 675–695 (1977)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A fast P system for finding a balanced 2-partition. Soft Computing 9, 673–678 (2005)CrossRefMATHGoogle Scholar
  4. 4.
    Păun, G.: P systems with active membranes: Attacking NP–complete problems. J. Automata, Languages and Combinatorics 6, 75–90 (2001)MathSciNetMATHGoogle Scholar
  5. 5.
    Păun, G., Suzuki, Y., Tanaka, H., Yokomori, T.: On the power of membrane division in P systems. Theoretical Computer Sci. 324, 61–85 (2004)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Pérez-Jiménez, M.J., Riscos-Núñez, A.: Solving the subset-sum problem by active membranes. New Generation Computing 23, 367–384 (2005)MATHGoogle Scholar
  7. 7.
    Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Complexity classes in cellular computing with membranes. Natural Computing 2, 265–285 (2003)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Computationally hard problems addressed through P systems. In: Ciobanu, G., et al. (eds.) Applications of Membrane Computing, pp. 315–346. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Sci. 8, 189–201 (1979)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Wegener, I.: Complexity Theory: Exploring the Limits of Efficient Algorithms. Springer, Heidelberg (2005)MATHGoogle Scholar
  12. 12.
    Williams, R.M., Wood, D.H.: Exascale computer algebra problems interconnect with molecular reactions and complexity theory. DIMACS Series in Discrete Mathematics and Theoretical Computer Sci. 44, 267–275 (1999)MathSciNetMATHGoogle Scholar
  13. 13.
  14. 14.
  15. 15.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Artiom Alhazov
    • 1
  • Liudmila Burtseva
    • 1
  • Svetlana Cojocaru
    • 1
  • Yurii Rogozhin
    • 1
    • 2
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Research Group on Mathematical LinguisticsRovira i Virgili UniversityTarragonaSpain

Personalised recommendations