On a Powerful Class of Non-universal P Systems with Active Membranes

  • Antonio E. Porreca
  • Alberto Leporati
  • Claudio Zandron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)

Abstract

We prove that uniform and semi-uniform families of P systems with active membranes using only communication and nonelementary division rules are not computationally universal. However, they are powerful enough to solve exactly the problems solvable by Turing machines operating in time and space that are ”tetrational” (i.e., bounded by a stack of exponentials of polynomial height) with respect to the size of the input.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chung, F.R.K., Graham, R.L., Coppersmith, D.: On trees containing all small trees. In: Chartrand, G. (ed.) The Theory of Applications of Graphs, pp. 265–272. Wiley, Chichester (1981)Google Scholar
  2. 2.
    Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Mathematical Systems Theory 2(3), 265–283 (1968)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hartmanis, J., Stearns, R.E.: On the computational complexity of algorithms. Transactions of the American Mathematical Society 117, 285–306 (1965)MATHMathSciNetGoogle Scholar
  4. 4.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 1(61), 108–143 (2000)CrossRefGoogle Scholar
  5. 5.
    Păun, G.: P systems with active membranes: Attacking NP-complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)MATHMathSciNetGoogle Scholar
  6. 6.
    Păun, G.: Active membranes. In: Păun, G., Rozenberg, G., Salomaa, A. (eds.) The Oxford Handbook of Membrane Computing, pp. 282–301. Oxford University Press, Oxford (2010)Google Scholar
  7. 7.
    Păun, G., Rozenberg, G.: A guide to membrane computing. Theoretical Computer Science 287, 73–100 (2002)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)MATHGoogle Scholar
  9. 9.
    Pérez-Jiménez, M.J., Romero Jiménez, A., Sancho Caparrini, F.: Complexity classes in models of cellular computing with membranes. Natural Computing 2, 265–285 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: Introducing a space complexity measure for P systems. International Journal of Computers, Communications & Control 4(3), 301–310 (2009)Google Scholar
  11. 11.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: P systems with active membranes: Trading time for space. Natural Computing (to appear)Google Scholar
  12. 12.
    Porreca, A.E., Mauri, G., Zandron, C.: Complexity classes for membrane systems. RAIRO Theoretical Informatics and Applications 40(2), 141–162 (2006)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sosík, P.: The computational power of cell division in P systems: Beating down parallel computers? Natural Computing 2(3), 287–298 (2003)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    The P Systems Webpage, http://ppage.psystems.eu

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Antonio E. Porreca
    • 1
  • Alberto Leporati
    • 1
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly

Personalised recommendations