Encoding OCL Data Types for SAT-Based Verification of UML/OCL Models

  • Mathias Soeken
  • Robert Wille
  • Rolf Drechsler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6706)

Abstract

Checking the correctness of UML/OCL models is a crucial task in the design of complex software and hardware systems. As a consequence, several approaches have been presented which address this problem. Methods based on satisfiability (SAT) solvers have been shown to be very promising in this domain. Here, the actual verification task is encoded as an equivalent bit-vector instance to be solved by an appropriate solving engine. However, while a bit-vector encoding for basic UML/OCL constructs has already been introduced, no encoding for non-trivial OCL data types and operations is available so far. In this paper, we close this gap and present a bit-vector encoding for more complex OCL data types, i.e. sets, bags, and their ordered counterparts. As a result, SAT-based UML/OCL verification becomes applicable for models containing these collections types. A case study illustrates the application of this encoding.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rumbaugh, J., Jacobson, I., Booch, G.: The Unified Modeling Language reference manual. Addison-Wesley Longman, Essex (1999)Google Scholar
  2. 2.
    Vanderperren, Y., Müller, W., Dehaene, W.: UML for electronic systems design: a comprehensive overview. Design Automation for Embedded Systems 12(4), 261–292 (2008)CrossRefGoogle Scholar
  3. 3.
    Kyas, M., Fecher, H., de Boer, F.S., Jacob, J., Hooman, J., van der Zwaag, M., Arons, T., Kugler, H.: Formalizing UML Models and OCL Constraints in PVS. Electronic Notes in Theoretical Computer Science 115, 39–47 (2005)CrossRefGoogle Scholar
  4. 4.
    Beckert, B., Hähnle, R., Schmitt, P.: Verification of Object-Oriented Software: The KeY Approach. Springer, Secaucus (2007)MATHGoogle Scholar
  5. 5.
    Gogolla, M., Kuhlmann, M., Hamann, L.: Consistency, Independence and Consequences in UML and OCL Models. In: Tests and Proof, pp. 90–104. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Cabot, J., Clarisó, R., Riera, D.: Verification of UML/OCL Class Diagrams using Constraint Programming. In: IEEE Int. Conf. on Software Testing Verification and Validation Workshop, pp. 73–80 (April 2008)Google Scholar
  7. 7.
    Cabot, J., Clarisó, R., Riera, D.: Verifying UML/OCL Operation Contracts. In: Leuschel, M., Wehrheim, H. (eds.) IFM 2009. LNCS, vol. 5423, pp. 40–55. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Anastasakis, K., Bordbar, B., Georg, G., Ray, I.: UML2Alloy: A Challenging Model Transformation. In: Int. Conf. on Model Driven Engineering Languages and Systems, pp. 436–450. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Soeken, M., Wille, R., Kuhlmann, M., Gogolla, M., Drechsler, R.: Verifying UML/OCL models using Boolean satisfiability. In: Design, Automation and Test in Europe, pp. 1341–1344. IEEE Computer Society, Los Alamitos (2010)Google Scholar
  10. 10.
    Soeken, M., Wille, R., Drechsler, R.: Verifying Dynamic Aspects of UML Models. In: Design, Automation and Test in Europe. IEEE Computer Society, Los Alamitos (2011)Google Scholar
  11. 11.
    Warmer, J., Kleppe, A.: The Object Constraint Language: Precise modeling with UML. Addison-Wesley Longman, Boston (1999)Google Scholar
  12. 12.
    Constantinides, G.A., Cheung, P.Y.K., Luk, W.: Synthesis of Saturation Arithmetic Architectures. ACM Trans. Design Autom. Electr. Syst. 8(3), 334–354 (2003)CrossRefGoogle Scholar
  13. 13.
    Cook, S.A.: The complexity of theorem-proving procedures. In: ACM Symp. on Theory of Computing, pp. 151–158. ACM, New York (1971)Google Scholar
  14. 14.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Design Automation Conference, pp. 530–535. ACM, New York (2001)Google Scholar
  15. 15.
    Goldberg, E.I., Novikov, Y.: BerkMin: A Fast and Robust Sat-Solver. In: Design, Automation and Test in Europe, pp. 142–149. IEEE Computer Society, Los Alamitos (2002)Google Scholar
  16. 16.
    Eén, N., Sörensson, N.: An Extensible SAT-solver. Theory and Applications of Satisfiability Testing, 502–518 (May 2003)Google Scholar
  17. 17.
    Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, February 2009. IOS Press, Amsterdam, NL (February 2009)MATHGoogle Scholar
  18. 18.
    Armando, A., Castellini, C., Giunchiglia, E.: SAT-Based Procedures for Temporal Reasoning. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, pp. 97–108. Springer, Heidelberg (2000)Google Scholar
  19. 19.
    Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast Decision Procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Wille, R., Große, D., Soeken, M., Drechsler, R.: Using Higher Levels of Abstraction for Solving Optimization Problems by Boolean Satisfiability. In: IEEE Symp. on VLSI, pp. 411–416. IEEE Computer Society, Los Alamitos (2008)Google Scholar
  21. 21.
    Brummayer, R., Biere, A.: Boolector: An Efficient SMT Solver for Bit-Vectors and Arrays. In: Tools and Algorithms for Construction and Analysis of Systems, pp. 174–177. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Jackson, D., Damon, C.: Elements of Style: Analyzing a Software Design Feature with a Counterexample Detector. IEEE Trans. on Software Engineering 22(7), 484–495 (1996)CrossRefGoogle Scholar
  23. 23.
    Davenport, J.H., Heintz, J.: Real Quantifier Elimination is Doubly Exponential. Journal of Symbolic Computation 5(1-2), 29–35 (1988)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mathias Soeken
    • 1
  • Robert Wille
    • 1
  • Rolf Drechsler
    • 1
  1. 1.Computer Architecture GroupInstitute of Computer Science, University of BremenBremenGermany

Personalised recommendations