On the Dynamics of PB Systems: A Petri Net View

  • Silvano Dal Zilio
  • Enrico Formenti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2933)


We study dynamical properties of PB systems, a new computational model of biological processes, and propose a compositional encoding of PB systems into Petri nets. Building on this relation, we show that three properties: boundedness, reachability and cyclicity, which we claim are useful in practice, are all decidable.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bernardini, F., Manca, V.: Dynamical aspects of P systems. BioSystems 70(2), 85–93 (2003)CrossRefGoogle Scholar
  2. 2.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity results for 1-safe nets. Theoretical Computer Science 147(1&2), 117–136 (1995)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Esparza, J., Nielsen, M.: Decibility issues for Petri nets - a survey. Journal of Informatik Processing and Cybernetics 30(3), 143–160 (1994)MATHGoogle Scholar
  5. 5.
    Haas, P.: Stochastic Petri Nets: Modelling, Stability, Simulation. Springer, Heidelberg (2002)MATHGoogle Scholar
  6. 6.
    Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and System Sciences 3, 147–195 (1969)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Lipton, R.J.: The reachability problem requires exponential space. Technical Report 62, Department of Computer Science, Yale University (1976)Google Scholar
  8. 8.
    Memmi, G., Roucairol, G.: Linear algebra in net theory. In: Brauer, W. (ed.) Net Theory and Applications. LNCS, vol. 84, pp. 213–223. Springer, Heidelberg (1980)Google Scholar
  9. 9.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Păun, G.: Computing with membranes (P systems): An introduction. Bulletin of EATCS 68, 139–152 (1999)Google Scholar
  11. 11.
    Păun, G.: Membrane Computing: An Introduction. Springer, New York (2002)MATHGoogle Scholar
  12. 12.
    Peterson, J.L.: Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cliffs (1981)MATHGoogle Scholar
  13. 13.
    Reinhardt, K.: Das Erreichbarkeitproblem bei Petrinetzen mit inhibitorischen Kanten (1994) (unpublished manuscript)Google Scholar
  14. 14.
    Reisig, W.: Petri Nets, An Introduction. In: EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)Google Scholar
  15. 15.
    Wang, J.: Timed Petri Nets, Theory and Application. Kluwer Academic Publishers, Dordrecht (1998)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Silvano Dal Zilio
    • 1
  • Enrico Formenti
    • 2
  1. 1.Laboratoire d’Informatique Fondamentale de MarseilleCNRS and Université de ProvenceFrance
  2. 2.I3S – Université de Nice Sophia-AntipolisFrance

Personalised recommendations