Skip to main content
SpringerLink
Log in

Satisfiability Solvers Are Static Analysers

  • Conference paper
Static Analysis (SAS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7460))

Included in the following conference series:

Abstract

This paper shows that several propositional satisfiability algorithms compute approximations of fixed points using lattice-based abstractions. The Boolean Constraint Propagation algorithm (bcp) is a greatest fixed point computation over a lattice of partial assignments. The original algorithm of Davis, Logemann and Loveland refines bcp by computing a set of greatest fixed points. The Conflict Driven Clause Learning algorithm alternates between overapproximate deduction with bcp, and underapproximate abduction, with conflict analysis. Thus, in a precise sense, satisfiability solvers are abstract interpreters. Our work is the first step towards a uniform framework for the design and implementation of satisfiability algorithms, static analysers and their combination.

Supported by the Toyota Motor Corporation, EPSRC project EP/H017585/1 and ERC project 280053.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ball, T., Majumdar, R., Millstein, T.D., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: PLDI, pp. 203–213. ACM Press (2001)

    Google Scholar 

  2. Beckman, N.E., Nori, A.V., Rajamani, S.K., Simmons, R.J.: Proofs from tests. In: Proc. of Software Testing and Analysis, pp. 3–14. ACM Press (2008)

    Google Scholar 

  3. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. JACM 50, 752–794 (2003)

    Article  MathSciNet  Google Scholar 

  4. Cousot, P.: Abstract interpretation. MIT Course 16.399 (February-May 2005)

    Google Scholar 

  5. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252. ACM Press (1977)

    Google Scholar 

  6. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL, pp. 269–282. ACM Press (1979)

    Google Scholar 

  7. Cousot, P., Cousot, R.: Abstract interpretation and application to logic programs. Journal of Logic Programming 13(2-3), 103–179 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cousot, P., Cousot, R.: Abstract interpretation frameworks. Journal of Logic and Computation 2(4), 511–547 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cousot, P., Cousot, R., Mauborgne, L.: The Reduced Product of Abstract Domains and the Combination of Decision Procedures. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 456–472. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. CACM 5, 394–397 (1962)

    MathSciNet  MATH  Google Scholar 

  11. Davis, M., Putnam, H.: A computing procedure for quantification theory. JACM 7, 201–215 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  12. D’Silva, V., Haller, L., Kroening, D., Tautschnig, M.: Numeric Bounds Analysis with Conflict-Driven Learning. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 48–63. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Granger, P.: Improving the Results of Static Analyses Programs by Local Decreasing Iteration (Extended Abstract). In: Shyamasundar, R. (ed.) FSTTCS 1992. LNCS, vol. 652, pp. 68–79. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  14. Gulavani, B.S., Chakraborty, S., Nori, A.V., Rajamani, S.K.: Automatically Refining Abstract Interpretations. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 443–458. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Holley, L.H., Rosen, B.K.: Qualified data flow problems. In: POPL, pp. 68–82. ACM Press, New York (1980)

    Google Scholar 

  16. Kildall, G.A.: A unified approach to global program optimization. In: POPL, pp. 194–206. ACM, New York (1973)

    Google Scholar 

  17. King, J.C.: A Program Verifier. PhD thesis (1969)

    Google Scholar 

  18. McMillan, K.L.: Lazy Annotation for Program Testing and Verification. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 104–118. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). JACM 53, 937–977 (2006)

    Article  MathSciNet  Google Scholar 

  20. Rival, X., Mauborgne, L.: The trace partitioning abstract domain. TOPLAS 29(5), 26 (2007)

    Article  Google Scholar 

  21. Robinson, J.A.: A machine-oriented logic based on the resolution principle. JACM 12(1), 23–41 (1965)

    Article  MATH  Google Scholar 

  22. Silva, J.P.M., Sakallah, K.A.: GRASP – a new search algorithm for satisfiability. In: ICCAD, pp. 220–227 (1996)

    Google Scholar 

  23. Sörensson, N., Biere, A.: Minimizing Learned Clauses. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 237–243. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  24. Thakur, A., Reps, T.: A Generalization of Stålmarck’s Method. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 334–351. Springer, Heidelberg (2012)

    Google Scholar 

  25. Thakur, A., Reps, T.: A Method for Symbolic Computation of Abstract Operations. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 174–192. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  26. Wegman, M.N., Zadeck, F.K.: Constant propagation with conditional branches. TOPLAS 13, 181–210 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Oxford University, UK

    Vijay D’Silva, Leopold Haller & Daniel Kroening

Authors
  1. Vijay D’Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leopold Haller
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Kroening
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45, rue d’Ulm, 75005, Paris, France

    Antoine Miné

  2. Department of Computing and Information Sciences, Kansas State University, 234 Nichols Hall, 66506, Manhattan, KS, USA

    David Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

D’Silva, V., Haller, L., Kroening, D. (2012). Satisfiability Solvers Are Static Analysers. In: Miné, A., Schmidt, D. (eds) Static Analysis. SAS 2012. Lecture Notes in Computer Science, vol 7460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33125-1_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33125-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33124-4

  • Online ISBN: 978-3-642-33125-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation