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Representing and Approximating Transfer Functions in Abstract Interpretation of Hetereogeneous Datatypes

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Static Analysis (SAS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2477))

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Abstract

We present a general method to combine different datatypes in Abstract Interpretation, within the framework of verification of reactive system. We focus more precisely on the efficient representation and approximation of the transfer functions involved in the abstract fix-point computations. The solution we propose allows to tune smoothly the necessary tradeoff between accuracy and efficiency in the analysis.

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References

  1. P. Aziz Abdulla, A. Bouajjani, and B. Jonsson. On-the-fly analysis of systems with unbounded, lossy fifo channels. In Computer Aided Verification, CAV’98, volume 1427 of LNCS, July 1998.

    Google Scholar 

  2. R. Bahar, E. Frohm, C. Gaona, G. Hachtel, E. Macii, A. Pardo, and F. Somenzi. Algebraic decision diagrams and their applications. Formal Methods in System Design, 10(2/3):171–206, April 1997.

    Google Scholar 

  3. G. Behrmann, K. G. Larsen, J. Pearson, C. Weise, and W. Yi. Efficient timed reachability analysis using clock difference diagrams. In Computer Aided Verification, CAV’99, volume 1633 of LNCS, July 1999.

    Chapter  Google Scholar 

  4. B. Boigelot and P. Godefroid. Symbolic verification of communication protocols with infinite state spaces using QDDs. In Computer Aided Verification, CAV’96, volume 1102 of LNCS, July 1996.

    Google Scholar 

  5. T. Bultan, R. Gerber, and C. League. Composite model checking: Verification with type-specific symbolic representations. ACM Transactions on Software Engineering and Methodology, 9(1), January 2000.

    Google Scholar 

  6. T. Bultan, R. Gerber, and W. Pugh. Symbolic model checking of infinite state systems using presburger arithmetic. In Computer Aided Verification, CAV’97, volume 1254 of LNCS, June 1997.

    Google Scholar 

  7. A. Cortesi, B. Le Charlier, and P. Van Hentenryck. Combination of abstract domains for logic programming: open product and generic pattern construct. Science of Computer Programming, 38, 2000.

    Google Scholar 

  8. P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In 4th ACM Symposium on Principles of Programming Languages, POPL’77, Los Angeles, January 1977.

    Google Scholar 

  9. P. Cousot and R. Cousot. Systematic design of program analysis frameworks. In 6th ACM Symposium on Principles of Programming Languages, POPL’79, San Antonio, January 1979.

    Google Scholar 

  10. P. Cousot and R. Cousot. Abstract interpretation frameworks. Journal of Logic and Computation, 1992.

    Google Scholar 

  11. R. Giacobazzi and E. Qintarelli. Incompleteness, counterexamples, and refinement in abstract model-checking. In Static Analysis Symposium, SAS’01, volume 2126 of LNCS, July 2001.

    Google Scholar 

  12. N. Halbwachs. Synchronous programming of reactive systems. Kluwer Academic Pub., 1993.

    Google Scholar 

  13. N. Halbwachs, P. Caspi, P. Raymond, and D. Pilaud. The synchronous dataflow programming language lustre. Proceedings of the IEEE, 79(9):1305–1320, September 1991.

    Google Scholar 

  14. N. Halbwachs, Y.E. Proy, and P. Roumanoff. Verification of real-time systems using linear relation analysis. Formal Methods in System Design, 11(2), August 1997.

    Google Scholar 

  15. T. Henzinger, P.-H. Ho, and H. Wong-Toï. HyTech: A Model Checker for Hybrid Systems. In Computer Aided Verification, CAV’97, number 1254 in LNCS, June 1997.

    Google Scholar 

  16. B. Jeannet. Dynamic partitioning in linear relation analysis. Application to the verification of reactive systems. Formal Methods in System Design. 40 pages, to appear, available as a BRICS Research Report http://www.brics.dk/RS/00/38.

  17. B. Jeannet, N. Halbwachs, and P. Raymond. Dynamic partitioning in analyses of numerical properties. In Static Analysis Symposium, SAS’99, volume 1694 of LNCS, Venezia (Italy), September 1999.

    Google Scholar 

  18. C. Mauras. Calcul symbolique et automates interprétés. Technical Report 10, IRCyN, November 1996.

    Google Scholar 

  19. J. Møller, J. Lichtenberg, H. R. Andersen, and H. Hulgaard. Difference decision diagrams. In Computer Science Logic, The IT University of Copenhagen, Denmark, September 1999.

    Google Scholar 

  20. G. Nelson and C. Oppen. Simplification by cooperating decision procedures. ACM Transactions on Programming Languages and Systems, 1(2), 1979.

    Google Scholar 

  21. F. Nielson. Tensor products generalize the relational data flow analysis method. In Fourth Hungarian Computer Science Conference, 1985.

    Google Scholar 

  22. F. Nielson and H. R. Nielson. The tensor product in wadler’s analysis of list. Science of Computer Programming, 22, 1994.

    Google Scholar 

  23. R. Shostak. Deciding combination of theories. Journal of the ACM, 31(1), 1984.

    Google Scholar 

  24. H. Sipma, T. Uribe, and Z. Manna. Model checking and deduction for infinite-state systems. In Logical Perspectives on Language and Information. CSLI publications, 2001.

    Google Scholar 

  25. T. Yavuz-Kahveci, M. Tuncer, and T. Bultan. A library for composite symbolic representations. In Tools and Algorithms for the Construction and Analysis of Systems, TACAS’01, volume 2031 of LNCS, April 2001.

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA-IRISA, France

    B. Jeannet

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  1. B. Jeannet
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Editor information

Editors and Affiliations

  1. Department of Computer Science Facultad de Informática, Technical University of Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain

    Manuel V. Hermenegildo  & Germán Puebla  & 

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Jeannet, B. (2002). Representing and Approximating Transfer Functions in Abstract Interpretation of Hetereogeneous Datatypes. In: Hermenegildo, M.V., Puebla, G. (eds) Static Analysis. SAS 2002. Lecture Notes in Computer Science, vol 2477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45789-5_7

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  • DOI: https://doi.org/10.1007/3-540-45789-5_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44235-6

  • Online ISBN: 978-3-540-45789-3

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