Advertisement

Verification of an Error Correcting Code by Abstract Interpretation

  • Charles Hymans
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3385)

Abstract

We apply the theory of abstract interpretation to validate a Reed Solomon error correcting code. We design and implement an abstract simulator for VHDL descriptions. This tool computes an over-approximation of all the states that would be reached during any run of a conventional simulator. It collects linear constraints that hold between signals in the design. It is used to check the RTL implementations of the Reed Solomon encoder and decoder against correct high-level specifications. We explain how to express the correctness property so as to defeat the state explosion incurred by the deep pipeline in the decoder. Benchmarks show the abstract simulator is very frugal in both memory and time. Comparisons with VIS confirm that specialized tools outperform general purpose algorithms. Abstract simulation also competes advantageously with simulation. In less time than what was allocated for simulation by the designers of the components, it achieves full coverage.

Keywords

Model Check Clock Cycle Error Correct Code Abstract Interpretation Abstract Domain 
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.
    ANSI/IEEE Std 1076-1987. IEEE Standard VHDL Language Reference Manual (1988)Google Scholar
  2. 2.
    IEEE Std 1164-1993. IEEE Standard Multivalue Logic System for VHDL Model Interoperability, (Std_logic_1164) (1993) Google Scholar
  3. 3.
    Accellera. Property Specification Language Reference Manual, Version 1.01 (2003), http://www.accellera.org/pslv101.pdf
  4. 4.
    Beer, I., Ben-David, S., Eisner, C., Fisman, D., Gringauze, A., Rodeh, Y.: The temporal logic sugar. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 363–367. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedure instead of BDDs. In: Proceedings of the 36th Design Automation Conference (DAC 1999), pp. 317–320. ACM Press, New York (1999)CrossRefGoogle Scholar
  6. 6.
    Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: A static analyzer for large safety-critical software. In: Conference on Programming Language Design and Implementation (PLDI 2003), pp. 196–207. ACM Press, New York (2003)CrossRefGoogle Scholar
  7. 7.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 35(8), 677–691 (1986)MATHCrossRefGoogle Scholar
  8. 8.
    Bryant, R.E.: Symbolic simulation - techniques and applications. In: Proceedings of the 27th ACM/IEEE Design Automation Conference (DAC 1990), pp. 517–521. IEEE Computer Society Press, Los Alamitos (1990)CrossRefGoogle Scholar
  9. 9.
    Burch, J.R., Clarke, E.M., Long, D.E., McMillan, K.L., Dill, D.L.: Symbolic model checking for sequential circuit verification. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 13(4), 401–424 (1994)CrossRefGoogle Scholar
  10. 10.
    Chou, C.-T.: The mathematical foundation of symbolic trajectory evaluation. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 196–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Clarke, E.M., Kroening, D., Yorav, K.: Behavioral consistency of C and verilog programs using bounded model checking. In: Proceedings of the 40th Design Automation Conference (DAC 2003), pp. 368–371. ACM Press, New York (2003)CrossRefGoogle Scholar
  12. 12.
    Cousot, P., Cousot, R.: 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 1977), pp. 238–252. ACM Press, New York (1977)CrossRefGoogle Scholar
  13. 13.
    Dijkstra, E.W.: Guarded commands, nondeterminacy and formal derivation of programs. Communications of the ACM 18(8), 453–457 (1975)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Granger, P.: Static analysis of linear congruence equalities among variables of a program. In: Proceedings of the International Joint Conference on Theory and Practice of Software Development (TAPSOFT 1991), vol.1 pp. 169–192 (1991) Google Scholar
  15. 15.
    The VIS Group. Vis: A system for verification and synthesis. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 428–432. Springer, Heidelberg (1996)Google Scholar
  16. 16.
    Horwitz, S., Demers, A.J., Teitelbaum, T.: An efficient general iterative algorithm for dataflow analysis. Acta Informatica 24(6), 679–694 (1987)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Hymans, C.: Checking Safety Properties of Behavioral VHDL Descriptions by Abstract Interpretation. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 444–460. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Hymans, C.: Design and Implementation of an Abstract Interpreter for VHDL. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 263–269. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Karr, M.: Affine relationships among variables of a program. Acta Informatica 6, 133–151 (1976)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Kildall, G.A.: A unified approach to global program optimization. In: 1st ACM Symposium on Principles of Programming Languages (POPL 1973), pp. 194–206 (1973)Google Scholar
  21. 21.
    Kölbl, A., Kukula, J.H., Damiano, R.F.: Symbolic RTL simulation. In: Proceedings of the 38th Design Automation Conference (DAC 2001), pp. 47–52. ACM Press, New York (2001)CrossRefGoogle Scholar
  22. 22.
    Leroy, X., Doligez, D., Garrigue, J., Rémy, D., Vouillon, J.: The Objective Caml System, Documentation and User’s Manual. INRIA-Institut National de Recherche en Informatique et en Automatique (2002)Google Scholar
  23. 23.
    Miné, A.: A few graph-based relational numerical abstract domains. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 117–132. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  24. 24.
    Plotkin, G.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Aarhus University (1981)Google Scholar
  25. 25.
    Reed, I.S., Solomon, G.: Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics 8, 300–304 (1960)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Seger, C.-J.H., Bryant, R.E.: Formal verification by symbolic evaluation of partially-ordered trajectories. Formal Methods in System Design 6(2), 147–189 (1995)CrossRefGoogle Scholar
  27. 27.
    Simon, A., King, A., Howe, J.M.: Two variables per linear inequality as an abstract domain. In: Logic Based Program Synthesis and Tranformation (LOPSTR 2002), pp. 71–89 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Charles Hymans
    • 1
  1. 1.STIXÉcole PolytechniquePalaiseauFrance

Personalised recommendations