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)

Abstract

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.

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References

  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

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