Module: ppl/ppl Branch: master Commit: fdcab35567fd8b9031b4dff2e968476485f74ebd URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=fdcab35567fd8...

Author: Roberto Bagnara roberto.bagnara@bugseng.com Date: Sun Dec 29 10:12:27 2013 +0100

Fixed KapurZHZLN13.

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doc/ppl_citations.bib | 25 ++++++++++++++----------- 1 files changed, 14 insertions(+), 11 deletions(-)

diff --git a/doc/ppl_citations.bib b/doc/ppl_citations.bib index 1df5397..1c0c7fa 100644 --- a/doc/ppl_citations.bib +++ b/doc/ppl_citations.bib @@ -3183,8 +3183,10 @@ Summarizing: }

@InCollection{KapurZHZLN13, - Author = "D. Kapur and Z. Zhang and M. Horbach and H. Zhao and Q. Lu and T. Nguyen", - Title = "Geometric Quantifier Elimination Heuristics for Automatically Generating Octagonal and Max-plus Invariants", + Author = "D. Kapur and Z. Zhang and M. Horbach and H. Zhao and Q. Lu + and T. Nguyen", + Title = "Geometric Quantifier Elimination Heuristics + for Automatically Generating Octagonal and Max-plus Invariants", Booktitle = "Automated Reasoning and Mathematics: Essays in Memory of William W. McCune", Editor = "M. P. Bonacina and M. E. Stickel", @@ -3197,26 +3199,27 @@ Summarizing: Abstract = "Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly - relational numerical properties (such as l =< x =< h or - l =< +/- x +/- y =< h) for imperative programs. Such properties + relational numerical properties (such as $l \leq x \leq h$ or + $l \leq  \pm x \pm y \leq h)$ for imperative programs. + Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astr'ee tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract - interpretation approach (O(n^2) in contrast to O(n^4), - where n is the number of variables) with the ability to + interpretation approach ($O(n^2)$ in contrast to $O(n^4)$, + where $n$ is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum - function (such as max (x + a,y + b,z + c,d) ≤ max - (x + e,y + f,z + g,h)), thus enabling automatic - generation of a subclass of disjunctive invariants for - imperative programs as well." + function (such as + $\max(x + a, y + b, z + c, d) \leq \max (x + e, y + f, z + g, h)$), + thus enabling automatic generation of a subclass of + disjunctive invariants for imperative programs as well." }

-@Incollection {KhalilGP09, +@Incollection{KhalilGP09, Author = "G. Khalil and E. Goubault and S. Putot", Title = "The Zonotope Abstract Domain {Taylor1+}", Booktitle = "Computer Aided Verification: