Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Verification, Model Checking, and Abstract Interpretation

VMCAI 2009: Verification, Model Checking, and Abstract Interpretation pp 245–259Cite as

Deciding Extensions of the Theories of Vectors and Bags

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5403))

Abstract

Vectors and bags are basic collection data structures, which are used frequently in programs and specifications. Reasoning about these data structures is supported by established algorithms for deciding ground satisfiability in the theories of arrays (for vectors) and multisets (for bags), respectively. Yet, these decision procedures are only able to reason about vectors and bags in isolation, not about their combination.

This paper presents a decision procedure for the combination of the theories of vectors and bags, even when extended with a function bagof bridging between vectors and bags. The function bagof converts vectors into the bags of their elements, thus admitting vector/bag comparisons. Moreover, for certain syntactically restricted classes of ground formulae decidability is retained if the theory of vectors is extended further with a map function which applies uninterpreted functions to all elements of a vector.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aspinall, D., Maier, P., Stark, I.: Monitoring external resources in Java MIDP. Electr. Notes Theor. Comput. Sci. 197(1), 17–30 (2008)

    Article  Google Scholar 

  2. Aspinall, D., Maier, P., Stark, I.: Safety guarantees from explicit resource management. In: Proc. FMCO 2007. LNCS, vol. 5382, pp. 52–71. Springer, Heidelberg (2008)

    Google Scholar 

  3. Bradley, A.R., Manna, Z., Sipma, H.B.: What’s decidable about arrays? In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 427–442. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Ghilardi, S., Nicolini, E., Ranise, S., Zucchelli, D.: Decision procedures for extensions of the theory of arrays. Ann. Math. Artif. Intell. 50(3-4), 231–254 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On local reasoning in verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245–257 (1979)

    Article  MATH  Google Scholar 

  7. Piskac, R., Kuncak, V.: Decision procedures for multisets with cardinality constraints. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 218–232. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Piskac, R., Kuncak, V.: Linear arithmetic with stars. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 268–280. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Sofronie-Stokkermans, V.: Hierarchic reasoning in local theory extensions. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 219–234. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Suzuki, N., Jefferson, D.: Verification decidability of Presburger array programs. J. ACM 27(1), 191–205 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tinelli, C., Zarba, C.G.: Combining decision procedures for sorted theories. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229, pp. 641–653. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Zarba, C.G.: Combining multisets with integers. In: Voronkov, A. (ed.) CADE 2002. LNCS, vol. 2392, pp. 363–376. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Foundations of Computer Science School of Informatics, The University of Edinburgh, Scotland

    Patrick Maier

Authors
  1. Patrick Maier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. (Emeritus University of Copenhagen), Bukkeballevej 88, 2960, Rungsted, Denmark

    Neil D. Jones

  2. Institut für Informatik, Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität, 48149, Münster, Germany

    Markus Müller-Olm

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maier, P. (2008). Deciding Extensions of the Theories of Vectors and Bags. In: Jones, N.D., Müller-Olm, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2009. Lecture Notes in Computer Science, vol 5403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93900-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-93900-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93899-6

  • Online ISBN: 978-3-540-93900-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation