P Systems with Active Membranes Characterize PSPACE

  • Petr Sosík
  • Alfonso Rodríguez-Patón
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4287)

Abstract

A P system is a natural computing model inspired by information processes in cells and a control role of cellular membranes. We show that uniform families of P systems with active membranes are able to solve, in polynomial time, exactly the class of decisional problems PSPACE. Similar results were achieved also with other models of bio-inspired computers, such as DNA computing. Together they suggest that PSPACE naturally characterizes the computational potential of biological information processing.

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References

  1. 1.
    Păun, G.: Computing with Membranes. J. Comput. System Sci. 61, 108–143 (2000)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Păun, G.: Membrane Computing: an Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  3. 3.
    The P Systems Web Page at http://psystems.disco.unimib.it
  4. 4.
    Păun, G.: P systems with active membranes: attacking NP complete problems. J. Automata, Languages and Combinatorics 6(1), 75–90 (2001)MATHGoogle Scholar
  5. 5.
    Alhazov, A., Freund, R., Riscos-Núñez, A.: One and two polarizations, membrane creation and objects complexity in P systems. In: Ciobanu, G., Păun, G. (eds.) First Int. Workshop on Theory and Application of P Systems (TAPS), Timişoara, Romania, pp. 9–18 (2005)Google Scholar
  6. 6.
    Alhazov, A., Martin-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
  7. 7.
    Ciobanu, G., Pan, L., Păun, G., Pérez-Jiménez, M.J.: P Systems with Minimal Parallelism (submitted)Google Scholar
  8. 8.
    Pérez–Jiménez, M.J., Gutiérrez–Naranjo, M.A., Riscos–Núñez, A., Romero–Campero, F.J.: On the Power of Dissolution in P Systems with Active Membranes. In: Freund, R., et al. (eds.) WMC 2005. LNCS, vol. 3850, pp. 224–240. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A., Romero-Campero, F.J.: Characterizing standard tractability by cell-like membrane systems. In: Subramanian, K.G. (ed.) Formal Models, Languages and Applications, World Scientific, Singapore (in press, 2006)Google Scholar
  10. 10.
    Pérez-Jiménez, M.J., Jiménez, A.R., Sancho-Caparrini, F.: Complexity classes in models of cellular computing with membranes. Natural Computing 2, 265–285 (2003)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Sosík, P.: The computational power of cell division: beating down parallel computers? Natural Computing 2–3, 287–298 (2003)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    Balcazar, J.L., Diaz, J., Gabarro, J.: Structural Complexity II. Springer, Berlin (1991)Google Scholar
  14. 14.
    Beaver, D.: A universal molecular computer. In: Lipton, R.J., Baum, E.B. (eds.) DNA Based Computers. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, vol. 27, pp. 29–36 (1995)Google Scholar
  15. 15.
    Dantsin, E., Wolpert, A.: A robust DNA computation model that captures PSPACE. Int. J. Foundations Comp. Sci. 14(5), 933–951 (2003)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Pudlák, P.: Complexity theory and genetics: The computational power of crossing-over. Information and Computation 171, 201–223 (2001)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Petr Sosík
    • 1
    • 2
  • Alfonso Rodríguez-Patón
    • 1
  1. 1.Facultad de InformáticaUniversidad Politécnica de Madrid – UPMMadridSpain
  2. 2.Institute of Computer ScienceSilesian UniversityOpavaCzech Republic

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