On Commutativity Based Edge Lean Search

  • Dragan Bošnački
  • Edith Elkind
  • Blaise Genest
  • Doron Peled
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)


Exploring a graph through search is one of the most basic building blocks of various applications. In a setting with a huge state space, such as in testing and verification, optimizing the search may be crucial. We consider the problem of visiting all states in a graph where edges are generated by actions and the (reachable) states are not known in advance. Some of the actions may commute, i.e., they result in the same state for every order in which they are taken (this is the case when the actions are performed independently by different processes). We show how to use commutativity to achieve full coverage of the states while traversing considerably fewer edges.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basten, T., Bošnački, D., Geilen, M.: Cluster-based Partial Order Reduction. Automated Software Engineering 11(4), 365–402 (2004)CrossRefGoogle Scholar
  2. 2.
    Bošnački, D., Elkind, E., Genest, B., Peled, D.: On Commutativity Based Edge Lean Search (full version),
  3. 3.
    Păsăreanu, C.S., Dwyer, M.B., Huth, M.: Assume-Guarantee Model Checking of Software: A Comparative Case Study. In: Dams, D.R., Gerth, R., Leue, S., Massink, M. (eds.) Theoretical and Practical Aspects of SPIN Model Checking. LNCS, vol. 1680, Springer, Heidelberg (1999)Google Scholar
  4. 4.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  5. 5.
    Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems – An Approach to the State-Explosion Problem, PhD thesis, University of Liege, Computer Science Department (November 1994)Google Scholar
  6. 6.
    Godefroid, P., Wolper, P.: Using Partial Orders for the Efficient Verification of Deadlock Freedom and Safety Properties. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 176–185. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  7. 7.
    Godefroid, P., Holzmann, G., Pirottin, D.: State-Space Caching Revisited. Formal Methods in System Design 7(3), 227–242 (1995)CrossRefGoogle Scholar
  8. 8.
    Gouda, K., Zaki, M.J.: Efficiently Mining Maximal Feqent Itemsets. In: IEEE International Conference on Data Mining (ICDM 2001), pp. 163–170 (2001)Google Scholar
  9. 9.
    Holzmann, G.: The SPIN Model Checking. Addison Wesley, Reading (2003)Google Scholar
  10. 10.
    Koyuturk, M., Grama, A., Szpankowski, W.: An Efficient Algorithm for Detecting Frequent Subgraphs in Biological Networks. Bioinformatics 20, i200–i207 (2004)CrossRefGoogle Scholar
  11. 11.
    Mazurkiewicz, A.: Trace semantics. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Advances in Petri Nets. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1986)Google Scholar
  12. 12.
    Ochmanski, E.: Languages and Automata. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, pp. 167–204 (1995)Google Scholar
  13. 13.
    Peled, D.: Combining Partial Order Reductions with On-the-fly Model-Checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 377–390. Springer, Heidelberg (1994)Google Scholar
  14. 14.
    Valmari, A.: A Stubborn Attack on State Explosion. Formal Methods in System Design 1(4), 297–322 (1992)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dragan Bošnački
    • 1
  • Edith Elkind
    • 2
  • Blaise Genest
    • 3
  • Doron Peled
    • 4
  1. 1.Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB, EindhovenThe Netherlands
  2. 2.Department of Computer Science, University of SouthamptonUK
  3. 3.IRISA/CNRS, Campus de Beaulieu, 35042 Rennes CedexFrance
  4. 4.Department of Computer Science, Bar Ilan UniversityIsrael

Personalised recommendations