File:Combination of abstract domains.svg

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Summary

Description
English: Shows the analysis of a simple piece of C code (black) by abstract interpretation.
  • Red: set of values x can take in program executions. (Such sets cannot be represented in a computer due to the ellipses ("...") notation.)
  • Green: its abstraction by an interval.
  • Cyan: its abstraction by congruence classes mod 2.
Using in particular the latter abstraction, the possibility of a zero division can be excluded, since x is known to be non-even.
Date
Source Own work, created with converted to SVG via pdf2svg.
Author Jochen Burghardt
TeX source
\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=85mm,paperheight=70mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{30cm}
\setlength{\textheight}{26cm}
\setlength{\evensidemargin}{-2.7cm}
\setlength{\oddsidemargin}{-2.5cm}
\setlength{\parindent}{0cm}

\newcommand{\prog}{\tt}
\newcommand{\set}[1]{\{#1\}}
\newcommand{\Z}{Z\!\!\!\!Z}

\pagestyle{empty}

\begin{document}

\definecolor{ABST}{rgb}{0.00, 0.99, 0.99}
\definecolor{conc}{rgb}{0.99, 0.50, 0.50}
\definecolor{abst}{rgb}{0.00, 0.99, 0.00}

\newcommand{\co}[1]{\textcolor{conc}{#1}}
\newcommand{\ab}[1]{\textcolor{abst}{#1}}
\newcommand{\AB}[1]{\textcolor{ABST}{#1}}

$\begin{array}[t]{r@{}c@{} c @{}c@{}l r@{}c@{} c @{}c@{}l}
%
        &
        & \co{\Z}
        &
        &
        \\
%
        &
        & \ab{[-\infty,\infty]} , \AB{\set{0,1}}
        &
        &
        &
        \\
%
        &
        & \mbox{\prog if(x>0)}
        &
        &
        \\
%
        & {\scriptstyle\swarrow}
        &
        & {\scriptstyle\searrow}
        &
        \\
\co{\set{1,2,3,...}}
        &
        &
        &
        & \co{\set{...,\mbox-2,\mbox-1,0}}
        \\
\ab{[1,\infty]} , \AB{\set{0,1}}
        &
        &
        &
        & \ab{[-\infty,0]} , \AB{\set{0,1}}
        \\
\mbox{\prog x=2*x+1;}
        &
        & \mbox{\prog else}
        &
        & \mbox{\prog x=1-4*x;}
        \\
\co{\set{3,5,7,...}}
        &
        &
        &
        & \co{\set{1,3,5,...}}
        \\
\ab{[3,\infty]} , \AB{\set{1}}
        &
        &
        &
        & \ab{[1,\infty]} , \AB{\set{1}}
        \\
%
        & {\scriptstyle\searrow}
        &
        & {\scriptstyle\swarrow}
        &
        \\
%
        &
        & \co{\set{1,3,5,...}}
        &
        &
        &
        \\
%
        &
        & \ab{[1,\infty]} , \AB{\set{1}}
        &
        &
        \\
%
        &
        & \mbox{\prog x=8/(x\%2);}
        &
        &
        \\
\end{array}$
\end{document}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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30 December 2013

image/svg+xml

a2f0f434b9a8bf20ac12d5ef0641d30e4c1f50a3

47,441 byte

248 pixel

301 pixel

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Date/TimeThumbnailDimensionsUserComment
current13:51, 30 December 2013Thumbnail for version as of 13:51, 30 December 2013301 × 248 (46 KB)Jochen BurghardtUser created page with UploadWizard
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