Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2012: Tools and Algorithms for the Construction and Analysis of Systems pp 48–63Cite as

  1. Home
  2. Tools and Algorithms for the Construction and Analysis of Systems
  3. Conference paper
Numeric Bounds Analysis with Conflict-Driven Learning

Numeric Bounds Analysis with Conflict-Driven Learning

  • Vijay D’Silva18,
  • Leopold Haller18,
  • Daniel Kroening18 &
  • …
  • Michael Tautschnig18 
  • Conference paper
  • 1674 Accesses

  • 31 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7214)

Abstract

This paper presents a sound and complete analysis for determining the range of floating-point variables in control software. Existing approaches to bounds analysis either use convex abstract domains and are efficient but imprecise, or use floating-point decision procedures, and are precise but do not scale. We present a new analysis that elevates the architecture of a modern SAT solver to operate over floating-point intervals. In experiments, our analyser is consistently more precise than a state-of-the-art static analyser and significantly outperforms floating-point decision procedures.

Keywords

  • Decision Procedure
  • Interval Analysis
  • Abstract Interpretation
  • Abstract Domain
  • Bound Model Check

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.

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

Download conference paper PDF

References

  1. Aiken, A.: Introduction to set constraint-based program analysis. Science of Computer Programming 35, 79–111 (1999)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Balakrishnan, G., Sankaranarayanan, S., Ivančić, F., Gupta, A.: Refining the control structure of loops using static analysis. In: Proc. of the Intl. Conf. on Embedded Software, pp. 49–58. ACM Press (2009)

    Google Scholar 

  3. 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 

  4. Blanchet, B., Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Miné, A., Monniaux, D., Rival, X.: Design and Implementation of a Special-Purpose Static Program Analyzer for Safety-Critical Real-Time Embedded Software. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds.) The Essence of Computation. LNCS, vol. 2566, pp. 85–108. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  5. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-Guided Abstraction Refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)

    CrossRef  Google Scholar 

  6. Clarke, E., Kroning, D., Lerda, F.: A Tool for Checking ANSI-C Programs. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 168–176. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  7. Cotton, S.: Natural Domain SMT: A Preliminary Assessment. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 77–91. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  8. Cousot, P., Cousot, R.: Formal language, grammar and set-constraint-based program analysis by abstract interpretation. In: Proc. of Functional Programming Languages and Computer Architecture, pp. 170–181. ACM Press (June 1995)

    Google Scholar 

  9. Goubault, É., Putot, S.: Static Analysis of Numerical Algorithms. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 18–34. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  10. 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)

    CrossRef  Google Scholar 

  11. Gulavani, B.S., Rajamani, S.K.: Counterexample Driven Refinement for Abstract Interpretation. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 474–488. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  12. Gulwani, B.S., Jain, S., Koskinen, E.: Control-flow refinement and progress invariants for bound analysis. In: Proc. of Programming Language Design and Implementation, pp. 375–385. ACM Press (June 2009)

    Google Scholar 

  13. Harris, W.R., Sankaranarayanan, S., Ivančić, F., Gupta, A.: Program analysis via satisfiability modulo path programs. In: Proc. of Principles of Programming Languages, pp. 71–82. ACM Press (2010)

    Google Scholar 

  14. Jovanović, D., de Moura, L.: Cutting to the Chase Solving Linear Integer Arithmetic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 338–353. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  15. Korovin, K., Tsiskaridze, N., Voronkov, A.: Conflict Resolution. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 509–523. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  16. 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)

    CrossRef  Google Scholar 

  17. McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462–476. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  18. Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)

    CrossRef  MathSciNet  Google Scholar 

  19. Rival, X., Mauborgne, L.: The trace partitioning abstract domain. ACM Transactions on Programming Languages and Systems 29(5), 26 (2007)

    CrossRef  Google Scholar 

  20. Sankaranarayanan, S., Ivančić, F., Shlyakhter, I., Gupta, A.: Static Analysis in Disjunctive Numerical Domains. In: Yi, K. (ed.) SAS 2006. LNCS, vol. 4134, pp. 3–17. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  21. Siegel, S.F., Zirkel, T.K.: A functional equivalence verification suite for high-performance scientific computing. Technical Report UDEL-CIS-2011/02, Department of Computer and Information Sciences, University of Delaware (2011)

    Google Scholar 

  22. Simon, A., King, A.: Widening polyhedra with landmarks. In: Proc. of the Asian Symposium on Programming Languages and Systems, pp. 166–182 (2006)

    Google Scholar 

  23. Wang, C., Yang, Z., Gupta, A., Ivančić, F.: Using Counterexamples for Improving the Precision of Reachability Computation with Polyhedra. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 352–365. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Oxford, UK

    Vijay D’Silva, Leopold Haller, Daniel Kroening & Michael Tautschnig

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

  4. Michael Tautschnig
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California at Santa Cruz, 1156 High Street, 95064, Santa Cruz, CA, USA

    Cormac Flanagan

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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., Tautschnig, M. (2012). Numeric Bounds Analysis with Conflict-Driven Learning. In: Flanagan, C., König, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2012. Lecture Notes in Computer Science, vol 7214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28756-5_5

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-28756-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28755-8

  • Online ISBN: 978-3-642-28756-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature