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Program Verification Through Computer Algebra

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Book cover Formal Methods and Software Engineering (ICFEM 2006)

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

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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].

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References

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

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

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

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  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)

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  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)

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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
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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

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© 2006 Springer-Verlag Berlin Heidelberg

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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

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  • 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)

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