Skip to main content
SpringerLink
Log in

Solving Bit-Vector Equations

  • Conference paper
  • First Online:
Formal Methods in Computer-Aided Design (FMCAD 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1522))

Included in the following conference series:

Abstract

This paper is concerned with solving equations on fixed and non-fixed size bit-vector terms. We define an equational transformation system for solving equations on terms where all sizes of bit-vectors and extraction positions are known. This transformation system suggests a generalization for dealing with bit-vectors of unknown size and unknown extraction positions. Both solvers adhere to the principle of splitting bitvectors only on demand, thereby making them quite effective in practice.

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. C.W. Barrett, D.L. Dill, and J.R. Levitt. A Decision Procedure for Bit-Vector Arithmetic. In Proceedings of the 35th Design Automation Conference, June 1998. San Francisco, CA.

    Google Scholar 

  2. N.S. BjØrner and M.C. Pichora. Deciding Fixed and Non-Fixed Size Bit-Vectors. volume 1384 of Lecture Notes in Computer Science LNCS, pages 376–392, Heidelberg-New York-Berlin, April 1998. Springer.

    Google Scholar 

  3. D. Cyrluk, P. Lincoln, and N. Shankar. On Shostak’s Decision Procedure for Combinations of Theories. In A. cRobbie and J. K. Slaney, editors, Proceedings of the Thirteenth International Conference on Automated Deduction (CADE-96), volume 1104 of LNAI, pages 463–477, Berlin;Heidelberg;New York, 1996. Springer.

    Google Scholar 

  4. D. Cyrluk, M.O. Möller, and H. Rue\ An Efficient Decision Procedure for a Theory of Fixed-Size Bitvectors with Composition and Extraction. Ulmer Informatik-Berichte 96-08, FakultÄt für Informatik, UniversitÄt Ulm, 1996.

    Google Scholar 

  5. D. Cyrluk, M.O. Möller, and H. Rueff. An Efficient Decision Procedure for the Theory of Fixed-Sized Bit-Vectors. In O. Grumberg, editor, Computer Aided Verification. 9th International Conference (CAV97). Haifa, Israel, June 22–25, 1997: Proceedings, volume 1254 of Lecture Notes in Computer Science LNCS, pages 60–71, Berlin-Heidelberg-New York, 1997. Springer.

    Google Scholar 

  6. A. Degtyarev, Yu. Matiyasevich, and A. Voronkov. Simultaneous Rigid E-Unification is not so Simple. UPMAIL Technical Report 104, Uppsala University, Computing Science Department, 1995.

    Google Scholar 

  7. L. Lipshitz. The Diophantine Problem for Addition and Divisibility. Transactions of the American Mathematical Society, 235:271–283, January 1978.

    Google Scholar 

  8. L. Lipshitz. Some Remarks on the Diophantine Problem for Addition and Divisibility. Bull. Soc. Math. Belg. S’er. B, 33(1):41–52, 1981.

    MATH  MathSciNet  Google Scholar 

  9. G. S. Makanin. Investigations on equations in a free group. In K.U. Schulz, editor, Proceedings of Word Equations and Related Topics (IWWERT’ 90), volume 572 of LNCS, pages 1–11, Berlin;Heidelberg;New York, 1992. Springer.

    Google Scholar 

  10. M.O. Möller. Solving Bit-Vector Equations A Decision Procedure for Hardware Verification, 1998. Diploma Thesis, available from http://www.informatik.uni-ulm.de/~ki,Bitvector

  11. W. Plandowski and W. Rytter. Application of Lempel-Ziv Encodings to the Solution of Words Equations. In Proceedings of the 25th International Colloquium on Automata, Languages and Programming, ICALP’98, pages 731–742, July 1998. Aalborg, Denmark.

    Google Scholar 

  12. R.E. Shostak. Deciding Combinations of Theories. Journal of the ACM, 31(1):1–12, January 1984.

    Google Scholar 

  13. M.K. Srivas and S.P. Miller. Formal Verification of the AAMP5 Microprocessor. In M.G. Hinchey and J.P. Bowen, editors, Applications of Formal Methods, International Series in Computer Science, chapter 7, pages 125–180. Prentice Hall, Hemel Hempstead, UK, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Ny Munkegade, University of århus, building 540, DK - 8000, århus C, Denmark

    M. Oliver Möller

  2. Computer Science Laboratory, SRI International Computer Science, 333 Ravenswood Ave. Menlo Park, CA, 94025, USA

    Harald Rue\

Authors
  1. M. Oliver Möller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harald Rue\
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Utah, 50 S Central Campus, Salt Lake City, UT, 841112-9205, USA

    Ganesh Gopalakrishnan

  2. Department of Computer Science, Brigham Young University, 3361 TMCB, Provo, UT, 84602-6576, USA

    Phillip Windley

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Möller, M.O., Rue\, H. (1998). Solving Bit-Vector Equations. In: Gopalakrishnan, G., Windley, P. (eds) Formal Methods in Computer-Aided Design. FMCAD 1998. Lecture Notes in Computer Science, vol 1522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49519-3_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-49519-3_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65191-8

  • Online ISBN: 978-3-540-49519-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation