Monotonicity Analysis Can Speed Up Verification

  • Marcelo F. Frias
  • Rodolfo Gamarra
  • Gabriela Steren
  • Lorena Bourg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)


We introduce a strategy for the verification of relational specifications based on the analysis of monotonicity of variables within formulas. By comparing with the Alloy Analyzer, we show that for a relevant class of problems this technique outperforms analysis of the same problems using SAT-solvers, while consuming a fraction of the memory SAT-solvers require.


Binary Relation Total Order Memory Consumption Relational Logic Binary Decision Diagram 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bayardo Jr, R.J., Schrag, R.C.: Using CSP look-back techniques to solve real world SAT instances. In: Proc. of the 14th National Conf. on Artificial Intelligence, pp. 203–208 (1997)Google Scholar
  2. 2.
    Frias, M.F., Lopez Pombo, C.G., Baum, G.A., Aguirre, N., Maibaum, T.S.E.: Reasoning About Static and Dynamic Properties in Alloy: A Purely Relational Approach, to appear in ACM TOSEM (in press)Google Scholar
  3. 3.
    Goldberg, E., Novikov, Y.: BerkMin: a Fast and Robust SAT-Solver. In: Proceedings of DATE 2002, pp. 142–149 (2002)Google Scholar
  4. 4.
    Jackson, D.: Nitpick: A checkable specification language. In: Proceedings of the Workshop on Formal Methods in Software Practice, San Diego, Calif. (January 1996)Google Scholar
  5. 5.
    Jackson D.: Automating First-Order Relational Logic. In: Proceedings of SIGSOFT FSE 2000, Proc. ACM SIGSOFT Conf. Foundations of Software Engineering, San Diego, November 2000, pp. 130-139 (2000) Google Scholar
  6. 6.
    Jackson, D.: Alloy: A Lightweight Object Modelling Notation. ACM Transactions on Software Engineering and Methodology (TOSEM) 11(2), 256–290 (2002)CrossRefGoogle Scholar
  7. 7.
    Jackson, D., Jha, S., Damon, C.A.: Isomorph-Free Model Enumeration: A New Method for Checking Relational Specifications. ACM TOPLAS 20(2), 302–343 (1998)CrossRefGoogle Scholar
  8. 8.
    Jackson, D., Schechter, I., Shlyakhter, I.: Alcoa: the Alloy Constraint Analyzer. In: Proceedings of the International Conference on Software Engineering, Limerick, Ireland (June 2000)Google Scholar
  9. 9.
    Jackson, D., Shlyakhter, I., Sridharan, M.: A Micromodularity Mechanism. In: Proc. ACM SIGSOFT Conf. Foundations of Software Engineering/European Software Engineering Conference (FSE/ESEC 2001), Vienna (September 2001)Google Scholar
  10. 10.
    Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: 39th Design Automation Conference (DAC 2001), Las Vegas (June 2001)Google Scholar
  11. 11.
    Tarski, A., Givant, S.: A Formalization of Set Theory without Variables, vol. 41. A.M.S. Coll. Pub. (1987)Google Scholar
  12. 12.
    Wegener, I.: Branching Programs and Binary Decision Diagrams. In: SIAM Discrete Mathematics and Applications, SIAM, Philadelphia (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marcelo F. Frias
    • 1
  • Rodolfo Gamarra
    • 1
  • Gabriela Steren
    • 1
  • Lorena Bourg
    • 1
  1. 1.Department of Computer Science, School of Exact and Natural SciencesUniversidad de Buenos AiresArgentina

Personalised recommendations