Advertisement

Fast Synchronization in P Systems

  • Artiom Alhazov
  • Maurice Margenstern
  • Sergey Verlan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5391)

Abstract

We consider the problem of synchronizing the activity of all membranes of a P system. After pointing the connection with a similar problem dealt with in the field of cellular automata, where the problem is called the firing squad synchronization problem, FSSP for short, we provide two algorithms to solve this problem for P systems. One algorithm is non-deterministic and works in 2h + 3 steps, the other is deterministic and works in 3h + 3 steps, where h is the height of the tree describing the membrane structure.

Keywords

Root Node Cellular Automaton Intermediate Node Synchronization Problem Synchronization Algorithm 
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.
    Bernardini, F., Gheorghe, M., Margenstern, M., Verlan, S.: How to synchronize the activity of all components of a P system? In: Vaszil, G. (ed.) Proc. Intern. Workshop Automata for Cellular and Molecular Computing, MTA SZTAKI, Budapest, Hungary, pp. 11–22 (2007)Google Scholar
  2. 2.
    Goto, E.: A minimum time solution of the firing squad problem. Harward Univ. Course Notes for Applied Mathematics, 298 (1962)Google Scholar
  3. 3.
    Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. American Mathematical Society 7, 48–50 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mazoyer, J.: A six-state minimal time solution to the firing squad synchronization problem. Theoretical Science 50, 183–238 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  6. 6.
    Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    Prim, R.C.: Shortest connection networks and some generalizations. Bell System Technical Journal 36, 1389–1401 (1957)CrossRefGoogle Scholar
  8. 8.
    Spellman, P.T., Sherlock, G.: Reply whole-cell synchronization - effective tools for cell cycle studies. Trends in Biotechnology 22, 270–273 (2004)CrossRefGoogle Scholar
  9. 9.
    Umeo, H., Maeda, M., Fujiwara, N.: An efficient mapping scheme for embedding any one-dimensional firing squad synchronization algorithm onto two-dimensional arrays. In: Bandini, S., Chopard, B., Tomassini, M. (eds.) ACRI 2002. LNCS, vol. 2493, pp. 69–81. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Schmid, H., Worsch, T.: The firing squad synchronization problem with many generals for one-dimensional CA. In: Proc. IFIP TCS 2004, pp. 111–124 (2004)Google Scholar
  11. 11.
    Yunès, J.-B.: Seven-state solution to the firing squad synchronization problem. Theoretical Computer Sci. 127, 313–332 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    The P systems web page, http://ppage.psystems.eu

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Artiom Alhazov
    • 1
  • Maurice Margenstern
    • 2
  • Sergey Verlan
    • 1
    • 3
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Université Paul Verlaine - Metz, LITA, EA 3097, IUT de MetzMetz CédexFrance
  3. 3.LACL, Département InformatiqueUniversité Paris EstCréteilFrance

Personalised recommendations