Advertisement

Heuristic Search for the Analysis of Graph Transition Systems

  • Stefan Edelkamp
  • Shahid Jabbar
  • Alberto Lluch Lafuente
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)

Abstract

Graphs are suitable modeling formalisms for software and hardware systems involving aspects such as communication, object orientation, concurrency, mobility and distribution. State spaces of such systems can be represented by graph transition systems, which are basically transition systems whose states and transitions represent graphs and graph morphisms. Heuristic search is a successful Artificial Intelligence technique for solving exploration problems implicitly present in games, planning, and formal verification. Heuristic search exploits information about the problem being solved to guide the exploration process. The main benefits are significant reductions in the search effort and the size of solutions. We propose the application of heuristic search for the analysis of graph transition systems. We define algorithms and heuristics and present experimental results.

Keywords

Model Check Heuristic Search Graph Transformation Graph Grammar Reachability Problem 
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.
    Baldan, P., Corradini, A., König, B., König, B.: Verifying a behavioural logic for graph transformation systems. In: CoMeta 2003. ENTCS (2004)Google Scholar
  2. 2.
    Bonet, B., Geffner, H.: Planning as heuristic search. Artificial Intelligence 129(1–2), 5–33 (2001)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Caires, L., Cardelli, L.: A spatial logic for concurrency (part I). Inf. Comput. 186(2), 194–235 (2003)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cardelli, L., Gardner, P., Ghelli, G.: A spatial logic for querying graphs. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 597–610. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. The MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)MATHGoogle Scholar
  7. 7.
    Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Basic concepts and double push-out approach. In: Algebraic approaches to graph transformation, vol. 1. World Scientific, Singapore (1997)Google Scholar
  8. 8.
    Courcelle, B.: Handbook of graph grammars and computing by graph transformations. Foundations, ch. 5, vol. 1, pp. 313–400. World Scientific, Singapore (1997)CrossRefGoogle Scholar
  9. 9.
    Demmer, M.J., Herlihy, M.: The arrow distributed directory protocol. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 119–133. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Edelkamp, S.: Planning with pattern databases. In: ECP, pp. 13–24 (2001)Google Scholar
  11. 11.
    Edelkamp, S.: Taming numbers and durations in the model checking integrated planning system. JAIR 20, 195–238 (2003)MATHGoogle Scholar
  12. 12.
    Edelkamp, S., Jabbar, S., Lluch Lafuente, A.: Cost-algebraic heuristic search, pp. 1362–1367. AAAI, Menlo Park (2005)Google Scholar
  13. 13.
    Edelkamp, S., Leue, S., Lluch Lafuente, A.: Directed explicit-state model checking in the validation of communication protocols. STTT 5(2-3), 247–267 (2003)Google Scholar
  14. 14.
    Edelkamp, S., Lluch Lafuente, A.: Abstraction databases in theory and model checking practice. In: ICAPS Workshop on Connecting Planning Theory with Practice (2004)Google Scholar
  15. 15.
    Gadducci, F., Lluch Lafuente, A.: Graphical verification of a spatial logic for the pi-calculus. In: Graph Transformation for Verification and Concurrency. ENTCS (to appear, 2005)Google Scholar
  16. 16.
    Groce, A., Visser, W.: Model checking Java programs using structural heuristics. In: ISSTA. ACM Press, New York (2002)Google Scholar
  17. 17.
    Gyapay, S., Schmidt, Á., Varró, D.: Joint optimization and reachability analysis in graph transformation systems with time. In: GT-VMT. ENTCS, vol. 109, pp. 137–147. Elsevier, Amsterdam (2004)Google Scholar
  18. 18.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for heuristic determination of minimum path cost. IEEE Trans. on Systems Science and Cybernetics 4, 100–107 (1968)CrossRefGoogle Scholar
  19. 19.
    Henzinger, T., Jhala, R., Majumdar, R., Sutre, G.: Software verification with Blast. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 235–239. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Hirsch, D., Lluch Lafuente, A., Tuosto, E.: A logic for application level QoS. In: Proceedings of the 3rd Workshop on Quantitative Aspects of Programming LanguagesGoogle Scholar
  21. 21.
    Hoffmann, J., Nebel, B.: Fast plan generation through heuristic search. JAIR 14, 253–302 (2001)MATHGoogle Scholar
  22. 22.
    Holzmann, G.: The Spin Model Checker: Primer and Reference Manual. Addison-Wesley, Reading (2003)Google Scholar
  23. 23.
    Kastenberg, H., Rensink, A.: Model checking dynamic states in GROOVE. In: SPIN, pp. 299–305 (2006)Google Scholar
  24. 24.
    Korf, R.E.: Depth-first iterative-deepening: An optimal admissible tree search. Artificial Intelligence 27(1), 97–109 (1985)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Loiseaux, C., Graf, S., Sifakis, J., Bouajjani, A., Bensalem, S.: Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design 6, 1–35 (1995)CrossRefGoogle Scholar
  26. 26.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  27. 27.
    Pearl, J.: Heuristics. Addison-Wesley, Reading (1985)Google Scholar
  28. 28.
    Rensink, A.: Towards model checking graph grammars. In: Automated Verification of Critical Systems, Tech. Report DSSE-TR-2003, pp. 150–160 (2003)Google Scholar
  29. 29.
    Rensink, A.: Time and space issues in the generation of graph transition systems. In: GraBaTs. ENTCS, vol. 127, pp. 127–139. Elsevier, Amsterdam (2005)Google Scholar
  30. 30.
    Rensink, A., Distefano, D.: Abstract graph transformation. In: SVV. ENTCS (to appear, 2005)Google Scholar
  31. 31.
    Rozenberg, G. (ed.): Handbook of graph grammars and computing by graph transformations. World Scientific, Singapore (1997)MATHGoogle Scholar
  32. 32.
    Sobrinho, J.L.: Algebra and algorithms for QoS path computation and hop-by-hop routing in the internet. IEEE/ACM Trans. Netw. 10(4), 541–550 (2002)CrossRefGoogle Scholar
  33. 33.
    Varrò, D.: Automated formal verification of visual modeling languages by model checking. Journal on Software and Systems Modeling (2003)Google Scholar
  34. 34.
    Wegener, I.: Komplexitätstheorie. Springer, Heidelberg (2003) (in German)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Stefan Edelkamp
    • 1
  • Shahid Jabbar
    • 1
  • Alberto Lluch Lafuente
    • 2
  1. 1.Computer Science DepartmentUniversity of DortmundDortmundGermany
  2. 2. EmpoliItaly

Personalised recommendations