skip to main content
research-article

Multi-valued Simulation and Abstraction Using Lattice Operations

Authors Info & Claims
Published:02 January 2017Publication History
Skip Abstract Section

Abstract

Abstractions can cause spurious results, which need to be verified in the concrete system to gain conclusive results. Verification based on a multi-valued logic can distinguish between conclusive and inconclusive results, provides increased precision, and allows for encoding additional information into the model. To ensure a correct abstraction, one can use a mixed simulation [Meller et al. 2009]. We extend mixed simulation to include inconsistent values, thereby resolving an asymmetry and allowing for abstractions with increased precision when inconsistent values are available. In addition, we present a set of abstraction rules, compatible with the extended notion, for constructing abstract models.

References

  1. N. D. Belnap. 1977. Modern Uses of Multiple-Valued Logics. Reidel, 5--37.Google ScholarGoogle Scholar
  2. A. Bialynicki-Birula and H. Rasiowa. 1957. On the representation of quasi-Boolean algebras. Bull. Acad. Polon. Sci. Cl. III 5 (1957), 259--261, XXII.Google ScholarGoogle Scholar
  3. G. Bruns and P. Godefroid. 1999. Model checking partial state spaces with 3-valued temporal logics. In CAV, Lecture Notes in Computer Science, Vol. 1633. Springer, 274--287. Google ScholarGoogle ScholarCross RefCross Ref
  4. M. Chechik, B. Devereux, S. M. Easterbrook, and A. Gurfinkel. 2003. Multi-valued symbolic model-checking. ACM TOSEM 12, 4 (2003), 371--408. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. E. M. Clarke, O. Grumberg, S. Jha, Y. Lu, and H. Veith. 2000. Counterexample-guided abstraction refinement. In CAV, Lecture Notes in Computer Science, Vol. 1855. Springer, 154--169. Google ScholarGoogle ScholarCross RefCross Ref
  6. D. Dams, R. Gerth, and O. Grumberg. 1997. Abstract interpretation of reactive systems. ACM Trans. Program. Lang. Syst. 19, 2 (1997), 253--291. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. M. de Jonge and T. C. Ruys. 2010. The spinja model checker. In SPIN, Lecture Notes in Computer Science, Vol. 6349. Springer, 124--128. Google ScholarGoogle ScholarCross RefCross Ref
  8. M. Fitting. 1989. Bilattices and the theory of truth. J. Philos. Logic 18, 3 (1989), 225--256. Google ScholarGoogle ScholarCross RefCross Ref
  9. O. Grumberg. 2005. Abstraction and refinement in model checking. In FMCO, Lecture Notes in Computer Science, Vol. 4111. Springer, 219--242.Google ScholarGoogle Scholar
  10. A. Gurfinkel and M. Chechik. 2003. Multi-valued model checking via classical model checking. In CONCUR, Lecture Notes in Computer Science, Vol. 2761. Springer, 263--277. Google ScholarGoogle ScholarCross RefCross Ref
  11. A. Gurfinkel and M. Chechik. 2006. Why waste a perfectly good abstraction. In TACAS, Lecture Notes in Computer Science, Vol. 3920. Springer, 212--226. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. A. Gurfinkel, O. Wei, and M. Chechik. 2006. Yasm: A software model-checker for verification and refutation. In CAV, Lecture Notes in Computer Science, Vol. 4144. Springer, 170--174. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. M. Huth, R. Jagadeesan, and D. A. Schmidt. 2001. Modal transition systems: A foundation for three-valued program analysis. In ESOP, Lecture Notes in Computer Science, Vol. 2028. Springer, 155--169. Google ScholarGoogle ScholarCross RefCross Ref
  14. B. Konikowska and W. Penczek. 2002. Reducing model checking from multi-valued CTL* to CTL*. In CONCUR, Lecture Notes in Computer Science, Vol. 2421. Springer, 226--239. Google ScholarGoogle ScholarCross RefCross Ref
  15. D. Kozen. 1983. Results on the propositional mu-calculus. Theor. Comput. Sci. 27 (1983), 333--354. Google ScholarGoogle ScholarCross RefCross Ref
  16. S. A. Kripke. 1963. Semantical considerations on modal logic. Acta Philos. Fenn. 16 (1963).Google ScholarGoogle Scholar
  17. Y. Meller, O. Grumberg, and S. Shoham. 2009. A framework for compositional verification of multi-valued systems via abstraction-refinement. In ATVA, Lecture Notes in Computer Science, Vol. 5799. Springer, 271--288. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. C. J. H. Seger and R. E. Bryant. 1995. Formal verification by symbolic evaluation of partially-ordered trajectories. Formal Meth. Syst. Des. 6, 2 (1995), 147--189. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Y. Shramko, J. M. Dunn, and T. Takenaka. 2001. The trilattice of constructive truth values. J. Log. Comput. 11, 6 (2001), 761--788. Google ScholarGoogle ScholarCross RefCross Ref
  20. S. J. J. Vijzelaar and W. J. Fokkink. 2015. Multi-valued abstraction using lattice operations. In ACSD. IEEE Computer Society, 70--79. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. S. J. J. Vijzelaar, K. Verstoep, W. J. Fokkink, and H. E. Bal. 2011. Distributed MAP in the SpinJa model checker. In PDMC (EPTCS), Vol. 72. 84--90. Google ScholarGoogle ScholarCross RefCross Ref
  22. S. J. J. Vijzelaar, K. Verstoep, W. J. Fokkink, and H. E. Bal. 2014. Bonsai: Cutting models down to size. In PSI, Lecture Notes in Computer Science, Vol. 8974. Springer, 361--375.Google ScholarGoogle Scholar

Index Terms

  1. Multi-valued Simulation and Abstraction Using Lattice Operations

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Article Metrics

          • Downloads (Last 12 months)3
          • Downloads (Last 6 weeks)1

          Other Metrics

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader
        About Cookies On This Site

        We use cookies to ensure that we give you the best experience on our website.

        Learn more

        Got it!