Skip to main content
Springer Nature Link
Log in

Program Verification Through Computer Algebra

  • Conference paper
Formal Methods and Software Engineering (ICFEM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4260))

Included in the following conference series:

  • 693 Accesses

Abstract

This is to advocate the approach to reducing program verification to the algebraic symbolic computation. Recent advances indicate that various verification problems can be reduced to semi-algebraic systems (SAS for short), and resolved through computer algebra tools. In this talk, we report our encouraging attempts at applying DISCOVERER to program termination analysis and state reachability computation. DISCOVERER is a Maple program implementing an algorithm of real solution classification and isolation for SAS, which is based on the discovery of complete discrimination systems of parametric polynomials. The talk also concludes that this approach deserves further attention from the program verification community.

For theoretical and technical details of the work, we refer the reader to [1,2,3,4,5].

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

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  1. Xia, B., Yang, L.: An algorithm for isolating the real solutions of semi-algebraic systems. J. Symbolic Computation 34, 461–477 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Yang, L.: Recent advances on determining the number of real roots of parametric polynomials. J. Symbolic Computation 28, 225–242 (1999)

    Article  MATH  Google Scholar 

  3. Yang, L., Hou, X., Zeng, Z.: A complete discrimination system for polynomials. Science in China (Ser. E) 39, 628–646 (1996)

    MATH  MathSciNet  Google Scholar 

  4. Yang, L., Xia, B.: Real solution classifications of a class of parametric semi-algebraic systems. In: Proc. of Int’l Conf. on Algorithmic Algebra and Logic, pp. 281–289 (2005)

    Google Scholar 

  5. Yang, L., Zhan, N., Xia, B., Zhou, C.: Program verification by using DISCOVERER. In: Meyer, B., Woodcock, J. (eds.) VSTTE 2005. LNCS, vol. 4171, pp. 528–538. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Zhou Chaochen

Authors
  1. Zhou Chaochen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. International Institute of Software Technology, United Nations University, Macau, China

    Zhiming Liu

  2. Software Engineering Institute, East China Normal University, 200062, Shanghai, China

    Jifeng He

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chaochen, Z. (2006). Program Verification Through Computer Algebra. In: Liu, Z., He, J. (eds) Formal Methods and Software Engineering. ICFEM 2006. Lecture Notes in Computer Science, vol 4260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901433_1

Download citation

  • DOI: https://doi.org/10.1007/11901433_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47460-9

  • Online ISBN: 978-3-540-47462-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics