P Systems Simulating Oracle Computations

  • Antonio E. Porreca
  • Alberto Leporati
  • Giancarlo Mauri
  • Claudio Zandron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7184)

Abstract

We show how existing P systems with active membranes can be used as modules inside a larger P system; this allows us to simulate subroutines or oracles. As an application of this construction, which is (in principle) quite general, we provide a new, improved lower bound to the complexity class PMC\(_{\mathcal{AM}(-{\rm d},-{\rm n})}\) of problems solved by polynomial-time P systems with (restricted) elementary active membranes: this class is proved to contain PPP and hence, by Toda’s theorem, the whole polynomial hierarchy.

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References

  1. 1.
    Alhazov, A., Martín-Vide, C., Pan, L.: Solving a PSPACE-complete problem by recognizing P systems with restricted active membranes. Fundamenta Informaticae 58(2), 67–77 (2003)MathSciNetMATHGoogle Scholar
  2. 2.
    Murphy, N., Woods, D.: The computational power of membrane systems under tight uniformity conditions. Natural Computing 10(1), 613–632 (2011)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Complexity classes in models of cellular computing with membranes. Natural Computing 2(3), 265–284 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: Elementary active membranes have the power of counting. In: Martínez-del-Amor, M.A., Păun, G., Pérez-Hurtado, I., Romero-Campero, F.J., Valencia-Cabrera, L. (eds.) Ninth Brainstorming Week on Membrane Computing, No. 1/2011 in RGNC Reports, Fénix Editora, pp. 329–342 (2011), http://www.gcn.us.es/9BWMC/volume/24Porreca.pdf
  5. 5.
    Păun, G.: P systems with active membranes: Attacking NP-complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)MathSciNetMATHGoogle Scholar
  6. 6.
    Sosík, P.: The computational power of cell division in P systems: Beating down parallel computers? Natural Computing 2(3), 287–298 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Toda, S.: PP is as hard as the polynomial-time hierarchy. SIAM Journal on Computing 20(5), 865–877 (1991)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Valsecchi, A., Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: An Efficient Simulation of Polynomial-Space Turing Machines by P Systems with Active Membranes. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 461–478. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    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.) Proceedings of the Second International Conference Unconventional Models of Computation, UMC 2K, pp. 289–301. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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