Software Quality Journal

, Volume 24, Issue 1, pp 37–63 | Cite as

Accelerating temporal verification of Simulink diagrams using satisfiability modulo theories

Article

Abstract

Automatic verification of programs and computer systems with input variables represents a significant and well-motivated challenge. The case of Simulink diagrams is especially difficult, because there the inputs are read iteratively, and the number of input variables is in theory unbounded. We apply the techniques of explicit model checking to account for the temporal (control) aspects of verification and use set-based representation of data, thus handling both sources of non-determinism present in the verification. Two different representations of sets are evaluated in scalability with respect to the range of input variables. Explicit (enumerating) sets are very fast for small ranges but fail to scale. Symbolic sets, represented as first-order formulas in the bit-vector theory and compared using satisfiability modulo theory solvers, scale well to arbitrary (though still bounded) range of input variables. To leverage the combined strengths of explicit and symbolic representations, we have designed a hybrid representation which we showed to outperform both pure representations. Thus, the proposed method allows complete automatic verification without the need to limit the non-determinism of input. Moreover, the principle underlying the hybrid representation entails inferring knowledge about the system under verification, which the developers did not explicitly include in the system, and which can significantly accelerate the verification process.

Keywords

Formal verification Model checking Circuit analysis Satisfiability modulo theories 

Notes

Acknowledgments

The research leading to these results has received funding from the European Unions Seventh Framework Program (FP7/2007-2013) for CRYSTAL Critical System Engineering Acceleration Joint Undertaking under grant agreement Number 332830 and from specific national programs and/or funding authorities.

References

  1. Armando, A., Mantovani, J., & Platania, L. (2006). Bounded model checking of software using SMT solvers instead of SAT solvers. In SPIN, LNCS (Vol. 3925, pp. 146–162). New York: Springer. doi:10.1007/11691617_9.
  2. Barnat, J., & Bauch, P. (2013). Control explicit-data symbolic model checking: An introduction. Technical report, Masaryk University. http://arxiv.org/abs/1303.7379.
  3. Barnat, J., Beran, J., Brim, L., Kratochvíla, T., & Ročkai, P. (2012). Tool chain to support automated formal verification of avionics simulink designs. In FMICS, LNCS (Vol. 7437, pp. 78–92). New York: Springer. doi:10.1007/978-3-642-32469-7_6.
  4. Barnat, J., Brim, L., Havel, V., Havlíček, J., Kriho, J., Lenčo, M., et al. (2013). DiVinE 3.0—Explicit-state model-checker for multithreaded C/C++ programs. In CAV (pp. 863–868). doi:10.1007/978-3-642-39799-8_60.
  5. Barnat, J., Bauch, P., & Havel, V. (2014). Temporal verification of simulink diagrams. In Proceedings of the HASE (pp. 81–88). doi:10.1109/HASE.2014.20.
  6. Barrett, C., Stump, A., & Tinelli, C. (2010). The SMT-LIB standard: Version 2.0. Technical report, The University of Iowa.Google Scholar
  7. Biere, A., Cimatti, A., Clarke, E., Fujita, M., & Zhu, Y. (1999). Symbolic model checking using SAT procedures instead of BDDs. In Proceedings of the DAC (pp. 317–320). ACM. doi:10.1145/309847.309942.
  8. Bradley, A. (2011). SAT-based model checking without unrolling. In VMCAI (pp. 70–87). doi:10.1007/978-3-642-18275-4_7.
  9. Braione, P., Denaro, G., Křena, B., & Pezzè, M. (2008). Verifying LTL properties of bytecode with symbolic execution. In Proceedings of the bytecode (pp. 1–14). Elsevier Science.Google Scholar
  10. Bryant, R. (1991). On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication. IEEE Transactions on Computers, 40(2), 205–213. doi:10.1109/12.73590.MATHCrossRefGoogle Scholar
  11. Bryant, R., & Chen, Y. A. (1995). Verification of arithmetic circuits with binary moment diagrams. In Proceedings of the DAC (pp. 535–541). doi:10.1145/217474.217583.
  12. Bultan, T., Gerber, R., & Pugh, W. (1997). Symbolic model checking of infinite state systems using presburger arithmetic. In CAV, LNCS (Vol. 1254, pp. 400–411). New York: Springer. doi:10.1007/3-540-63166-6_39.
  13. Bultan, T., Gerber, R., & League, C. (1998). Verifying systems with integer constraints and Boolean predicates: A composite approach. In Proceedings of the ISSTA (pp. 113–123). doi:10.1145/271771.271799.
  14. Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., et al. (2002). NuSMV 2: An OpenSource tool for symbolic model checking. In CAV (pp. 241–268). doi:10.1007/3-540-45657-0_29.
  15. Clarke, E., Emerson, E., & Sistla, A. (1986). Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems, 8(2), 244–263. doi:10.1145/5397.5399.MATHCrossRefGoogle Scholar
  16. Cousot, P., & Cousot, R. (1977). Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In Proceedings of the POPL (pp. 238–252). ACM. doi:10.1145/512950.512973.
  17. de Moura, L., & Bjørner, N. (2008). Z3: An efficient SMT solver. In TACAS, LNCS (Vol. 4963, pp. 337–340). New York: Springer. doi:10.1007/978-3-540-78800-3_24.
  18. Duret-Lutz, A., Klai, K., Poitrenaud, D., & Thierry-Mieg, Y. (2011). Self-loop aggregation product—A new hybrid approach to on-the-fly LTL model checking. In ATVA, LNCS (Vol. 6996, pp. 336–350). New York: Springer. doi:10.1007/978-3-642-24372-1_24.
  19. Godefroid, P. (2003) Reasoning about abstract open systems with generalized module checking. In EMSOFT, LNCS (Vol. 2855, pp. 223–240). Springer. doi:10.1007/978-3-540-45212-6_15.
  20. Hagen, G., & Tinelli, C. (2008). Scaling up the formal verification of lustre programs with SMT-based techniques. In Proceedings of the FMCAD (pp. 1–9). doi:10.1109/FMCAD.2008.ECP.19.
  21. Halbwachs, N., Caspi, P., Raymond, P., & Pilaud, D. (1991). The synchronous data flow programming language LUSTRE. Proceedings of the IEEE, 79(9), 1305–1320. doi:10.1109/5.97300.CrossRefGoogle Scholar
  22. Hungar, H., Grumberg, O., & Damm, W. (1995). What if model checking must be truly symbolic. In CHARME, LNCS (Vol. 987, pp. 1–20). New York: Springer. doi:10.1007/3-540-60385-9_1.
  23. King, J. (1976). Symbolic execution and program testing. Communications of the ACM, 19(7), 385–394. doi:10.1145/360248.360252.MATHCrossRefGoogle Scholar
  24. Kroening, D., & Strichman, O. (2010). Decision procedures: An algorithmic point of view. New York: Springer.Google Scholar
  25. Kupferman, O., & Vardi, M. (1996). Module checking. In CAV, LNCS (Vol. 1102, pp. 75–86). New York: Springer. doi:10.1007/3-540-61474-5_59.
  26. Lin, H. (1996). Symbolic transition graph with assignment. In CONCUR, LNCS (Vol. 1119, pp. 50–65). New York: Springer. doi:10.1007/3-540-61604-7_47.
  27. McMillan, K. (1992). Symbolic model checking. Ph.D. thesis, Carnegie Mellon University.Google Scholar
  28. Meenakshi, B., Bhatnagar, A., & Roy, S. (2006). Tool for translating simulink models into input language of a model checker. In ICFEM, LNCS (Vol. 4260, pp. 606–620). New York: Springer. doi:10.1007/11901433_33.
  29. Miller, S., Anderson, E., Wagner, L., Whalen, M., & Heimdahl, M. (2005). Formal verification of flight critical software. In Proceedings of the GNC (pp. 1–16).Google Scholar
  30. Owicki, S., & Gries, D. (1976). An axiomatic proof technique for parallel programs I. Acta Informatica, 6, 319–340. doi:10.1007/BF00268134.MATHMathSciNetCrossRefGoogle Scholar
  31. Sebastiani, R., Tonetta, S., & Vardi, M. (2005). Symbolic systems, explicit properties: On hybrid approaches for LTL symbolic model checking. In CAV, LNCS (Vol. 3576, pp. 100–246). New York: Springer. doi:10.1007/11513988_35.
  32. Vardi, M., & Wolper, P. (1986). An automata—theoretic approach to automatic program verification. In Proceedings of the LICS (pp. 332–344). IEEE Computer Society Press.Google Scholar
  33. Williams, P., Biere, A., Clarke, E., & Gupta, A. (2000). Combining decision diagrams and SAT procedures for efficient symbolic model checking. In CAV, LNCS (Vol. 1855, pp. 124–138). New York: Springer. doi:10.1007/10722167_13.
  34. Wintersteiger, C., Hamadi, Y., & de Moura, L. (2013). Efficiently solving quantified bit-vector formulas. Formal Methods in System Design, 42(1), 3–23. doi:10.1007/s10703-012-0156-2.MATHCrossRefGoogle Scholar
  35. Xie, T., Marinov, D., Schulte, W., & Notkin, D. (2005). Symstra: A framework for generating object-oriented unit tests using symbolic execution. In TACAS, LNCS (Vol. 3440, pp. 365–381). New York: Springer. doi:10.1007/978-3-540-31980-1_24.
  36. Yang, Z., Wang, C., Gupta, A., & Ivančić, F. (2006). Mixed symbolic representations for model checking software programs. In Proceedings of the MEMOCODE (pp. 17–26). doi:10.1109/MEMCOD.2006.1695896.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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