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Sum of Abstract Domains

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NASA Formal Methods (NFM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9058))

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Abstract

In the abstract interpretation theory, program properties are encoded by abstract domains, and the combination of abstract domains leads to new properties to be analyzed. We propose a new method to combine numerical abstract domains based on the Minkowski sum. We provide a general framework equipped with all the necessary abstract operators for static analysis of imperative languages.

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References

  1. Amato, G., Di Nardo Di Maio, S., Scozzari, F.: Numerical static analysis with soot. In: Proceedings of the ACM SIGPLAN International Workshop on State of the Art in Java Program Analysis, SOAP (2013)

    Google Scholar 

  2. Amato, G., Scozzari, F.: Jandom. https://github.com/jandom-devel/Jandom

  3. Amato, G., Scozzari, F.: The abstract domain of parallelotopes. In: Proceedings of the NSAD 2012. ENTCS, vol. 287, pp. 17–28 (2012)

    Google Scholar 

  4. Amato, G., Scozzari, F.: Localizing widening and narrowing. In: Logozzo, F., Fähndrich, M. (eds.) Static Analysis. LNCS, vol. 7935, pp. 25–42. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Cortesi, A., Le Charlier, B., Van Hentenryck, P.: Combinations of abstract domains for logic programming: Open product and generic pattern construction. Science of Computer Programmming 38(1–3), 27–71 (2000)

    Article  MATH  Google Scholar 

  6. Cortesi, A., Filé, G., Winsborough, W.W.: The quotient of an abstract interpretation. Theoretical Computer Science 202(1–2), 163–192 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cousot, P., Cousot, R.: Static determination of dynamic properties of programs. In: Proc. 2nd Int’l Symposium on Programming, pp. 106–130 (1976)

    Google Scholar 

  8. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the POPL 1977, pp. 238–252 (1977)

    Google Scholar 

  9. Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: Proceedings of the POPL 1979, pp. 269–282 (1979)

    Google Scholar 

  10. Cousot, P., Cousot, R.: Abstract interpretation frameworks. Journal of Logic and Computation 2(4), 511–549 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of the POPL 1978, pp. 84–97 (1978)

    Google Scholar 

  12. Ghorbal, K., Ivančić, F., Balakrishnan, G., Maeda, N., Gupta, A.: Donut domains: efficient non-convex domains for abstract interpretation. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 235–250. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Goubault, E., Putot, S., Védrine, F.: Modular static analysis with zonotopes. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 24–40. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  14. Maisonneuve, V., Hermant, O., Irigoin, F.: Alice: a framework to improve affine loop invariant computation. In: 5th Workshop on Invariant Generation (2014)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  16. Sankaranarayanan, S., Sipma, H.B., Manna, Z.: Scalable analysis of linear systems using mathematical programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 25–41. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Correspondence to Francesca Scozzari .

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Amato, G., Di Nardo Di Maio, S., Scozzari, F. (2015). Sum of Abstract Domains. In: Havelund, K., Holzmann, G., Joshi, R. (eds) NASA Formal Methods. NFM 2015. Lecture Notes in Computer Science(), vol 9058. Springer, Cham. https://doi.org/10.1007/978-3-319-17524-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-17524-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17523-2

  • Online ISBN: 978-3-319-17524-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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