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An Iterative Method for Generating Loop Invariants

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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6681))

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Abstract

Automatic derivation of invariants is one of the critical conundrums in the framework of the inductive program verification methodologies. This paper presents a novel and simple approach to generating polynomial equations as loop invariants. Finite difference of expressions and linear equation solving are harnessed. Unlike related work, the generated constraints are linear equalities, which can be solved efficiently. Furthermore, invariants of higher degree can be constructed in terms of those of lower degree. The case studies demonstrate the effectiveness of the approach.

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References

  1. Bradley, A.R., Manna, Z., Sipma, H.B.: Termination of polynomial programs. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 113–129. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Chen, Y., Xia, B., Yang, L., Zhan, N.: Generating polynomial invariants with Discoverer and Qepcad. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) Formal Methods and Hybrid Real-Time Systems. LNCS, vol. 4700, pp. 67–82. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proc. POPL 1978, pp. 84–96 (1978)

    Google Scholar 

  4. Rodriguez-Carbonell, D.K.E.: Generating all polynomial invariants in simple loops. Journal of Symbolic Computation, 443–476 (2007)

    Google Scholar 

  5. Giacobazzi, R. (ed.): SAS 2004. LNCS, vol. 3148. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  6. Gulwani, S., Srivastava, S., Venkatesan, R.: Program analysis as constraint solving. In: Proc. PLDI 2008, pp. 281–292 (2008)

    Google Scholar 

  7. Kovács, L.: Reasoning algebraically about p-solvable loops. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 249–264. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Michael, H.S., Colon, A., Sankaranarayanan, S.: Linear Invariant Generation Using Non-linear Constraint Solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 420–433. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Miné, A.: The octagon abstract domain. Higher-Order and Symbolic Computation 19(1), 31–100 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Müller-Olm, M., Seidl, H.: Precise interprocedural analysis through linear algebra. In: POPL, pp. 330–341 (2004a)

    Google Scholar 

  11. Müller-Olm, M., Seidl, H.: Computing polynomial program invariants. Inf. Process. Lett. 91(5), 233–244 (2004b)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rodríguez-Carbonell, E., Kapur, D.: Automatic generation of polynomial invariants of bounded degree using abstract interpretation. Sci. Comput. Program. 64(1), 54–75 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sankaranarayanan, S., Sipma, H., Manna, Z.: Non-linear loop invariant generation using gröbner bases. In: POPL, pp. 318–329 (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, National University of Defense Technology, Changsha, 410073, China

    Shikun Chen & Mengjun Li

  2. School of Computer, BeiHang University, Beijing, 100083, China

    Zhoujun Li

  3. Dept. of Electrical and Computer Engineering, Portland State University, Portland, OR, 97207, USA

    Xiaoyu Song

Authors
  1. Shikun Chen
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  2. Zhoujun Li
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  3. Xiaoyu Song
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  4. Mengjun Li
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Purdue University, 305 North University Street, 47907, West Lafayette, IN, USA

    Mikhail Atallah

  2. Department of Computer Science, Illinois Institute of Technology, 60616, Chicago, IL, USA

    Xiang-Yang Li

  3. Department of Computer Science, Montana State University, EPS 357, 59717, Bozeman, MT, USA

    Binhai Zhu

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© 2011 Springer-Verlag Berlin Heidelberg

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Chen, S., Li, Z., Song, X., Li, M. (2011). An Iterative Method for Generating Loop Invariants. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-21204-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21203-1

  • Online ISBN: 978-3-642-21204-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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