P-Semiflow Computation with Decision Diagrams

  • Gianfranco Ciardo
  • Galen Mecham
  • Emmanuel Paviot-Adet
  • Min Wan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5606)


We present a symbolic method for p-semiflow computation, based on zero-suppressed decision diagrams. Both the traditional explicit methods and our new symbolic method rely on Farkas’ algorithm, and compute a generator set from which any p-semiflow for the Petri net can be derived through a linear combination. We demonstrate the effectiveness of four variants of our algorithm by applying them on a suite of Petri net models, showing that our symbolic approach can produce results in cases where the explicit approach is infeasible.


Minimal Support Outgoing Edge Explicit Approach Symbolic Method Nonterminal Node 
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  1. 1.
    Chiola, G., Franceschinis, G., Gaeta, R., Ribaudo, M.: GreatSPN 1.7: Graphical Editor and Analyzer for Timed and Stochastic Petri Nets. Performance Evaluation 24, 47–68 (1995)CrossRefzbMATHGoogle Scholar
  2. 2.
    Ciardo, G., Jones, R.L., Miner, A.S., Siminiceanu, R.: Logical and stochastic modeling with SMART. Performance Evaluation 63, 578–608 (2006)CrossRefGoogle Scholar
  3. 3.
    Colom, J.M., Silva, M.: Convex geometry and semiflows in P/T nets: A comparative study of algorithms for the computation of minimal p-semiflows. In: Proc. International Conference on Applications and Theory of Petri nets, pp. 74–95 (1989)Google Scholar
  4. 4.
    Colom, J., Silva, M.: Improving the linearly based characterization of P/T nets. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 113–145. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  5. 5.
    Farkas, J.: Theorie der einfachen ungleichungen. Journal für die reine und andgewandte Mathematik 124, 1–27 (1902)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Genrich, H.: Predicate/transition nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 207–247. Springer, Heidelberg (1987)Google Scholar
  7. 7.
    Govindarajan, R., Suciu, F., Zuberek, W.M.: Timed Petri net models of multithreaded multiprocessor architectures. In: Proc. Petri Nets and Performance Models, pp. 153–162 (1997)Google Scholar
  8. 8.
    Graf, S., Steffen, B., Lüttgen, G.: Compositional minimisation of finite state systems using interface specifications. Journal of Formal Aspects of Computing 8(5), 607–616 (1996)CrossRefzbMATHGoogle Scholar
  9. 9.
    Kimura, S., Clarke, E.M.: A parallel algorithm for constructing binary decision diagrams. In: Proc. International Conference on Computer Design, pp. 220–223. IEEE Comp. Soc. Press, Los Alamitos (1990)Google Scholar
  10. 10.
    Minato, S.-I.: Zero-suppressed BDDs and their applications. Software Tools for Technology Transfer 3, 156–170 (2001)zbMATHGoogle Scholar
  11. 11.
    Pastor, E., Roig, O., Cortadella, J., Badia, R.M.: Petri net analysis using boolean manipulation. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 416–435. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  12. 12.
    Wan, M., Ciardo, G.: Symbolic state-space generation of asynchronous systems using extensible decision diagrams. In: Nielsen, M., et al. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 582–594. Springer, Heidelberg (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gianfranco Ciardo
    • 1
  • Galen Mecham
    • 1
  • Emmanuel Paviot-Adet
    • 2
    • 3
  • Min Wan
    • 4
  1. 1.Dept. of Computer Science and EngineeringUniv. of CaliforniaRiverside
  2. 2.Université P. & M. Curie, LIP6 - CNRS UMRParisFrance
  3. 3.Université Paris Descartes, Inst. Univ. de TechnologieParisFrance
  4. 4.Yahoo! Inc.USA

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