Advertisement

On Reversibility and Determinism in P Systems

  • Artiom Alhazov
  • Kenichi Morita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5957)

Abstract

Membrane computing is a formal framework of distributed parallel computing. In this paper we study the reversibility and maximal parallelism of P systems from the computability point of view. The notions of reversible and strongly reversible systems are considered. The universality is shown for reversible P systems with either priorities or inhibitors, and a negative conjecture is stated for reversible P systems without such control. Strongly reversible P systems without control have shown to only generate sub-finite sets of numbers; this limitation does not hold if inhibitors are used.

Another concept considered is strong determinism, which is a syntactic property, as opposed to the determinism typically considered in membrane computing. Strongly deterministic P systems without control only accept sub-regular sets of numbers, while systems with promoters and inhibitors are universal.

Keywords

Cellular Automaton Priority Relation Reversible System Register Machine Terminal Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agrigoroaiei, O., Ciobanu, G.: Dual P Systems. In: Corne, D.W., Frisco, P., Paun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2008. LNCS, vol. 5391, pp. 95–107. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Bennett, C.H.: Logical reversibility of computation. IBM Journal of Research and Development 17, 525–532 (1973)MATHCrossRefGoogle Scholar
  3. 3.
    Calude, C., Păun, Gh.: Bio-steps beyond Turing. BioSystems 77, 175–194 (2004)CrossRefGoogle Scholar
  4. 4.
    Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theoret. Phys. 21, 219–253 (1982)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ibarra, O.H.: On strong reversibility in P systems and related problems (manuscript)Google Scholar
  6. 6.
    Leporati, A., Zandron, C., Mauri, G.: Reversible P systems to simulate Fredkin circuits. Fundam. Inform. 74(4), 529–548 (2006)MATHMathSciNetGoogle Scholar
  7. 7.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
  8. 8.
    Morita, K.: Universality of a reversible two-counter machine. Theoret. Comput. Sci. 168, 303–320 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Morita, K.: A simple reversible logic element and cellular automata for reversible computing. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 102–113. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Morita, K.: Simple universal one-dimensional reversible cellular automata. J. Cellular Automata 2, 159–165 (2007)MATHGoogle Scholar
  11. 11.
    Morita, K., Nishihara, N., Yamamoto, Y., Zhang, Zh.: A hierarchy of uniquely parsable grammar classes and deterministic acceptors. Acta Inf. 34(5), 389–410 (1997)Google Scholar
  12. 12.
    Morita, K., Yamaguchi, Y.: A universal reversible Turing machine. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 90–98. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  14. 14.
    P systems webpage, http://ppage.psystems.eu/

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Artiom Alhazov
    • 1
    • 2
  • Kenichi Morita
    • 1
  1. 1.IEC, Department of Information Engineering, Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova

Personalised recommendations