| author | Christian Urban <urbanc@in.tum.de> |
| Tue, 09 Oct 2018 08:16:25 +0100 | |
| changeset 574 | bd4f144326c7 |
| parent 538 | 17acdd516ccd |
| child 609 | e33545bb2eba |
| permissions | -rw-r--r-- |
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\documentclass[dvipsnames,14pt,t]{beamer}
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\usepackage{../slides}
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\usepackage{../langs}
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\usepackage{../graphics}
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\usepackage{../grammar}
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\usepackage{soul}
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\usepackage{mathpartir}
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% beamer stuff |
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\renewcommand{\slidecaption}{CFL 09, King's College London}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm] |
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\LARGE Compilers and \\[-2mm] |
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\LARGE Formal Languages (9)\\[3mm] |
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\end{tabular}}
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\normalsize |
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\ |
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Office: & N7.07 (North Wing, Bush House)\\ |
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Slides: & KEATS (also home work is there)\\ |
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\end{tabular}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\begin{center}
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\includegraphics[scale=0.6]{../pics/bridge-limits.png}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Old-Fashioned Eng.~vs.~CS}
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\begin{center}
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\begin{tabular}{@{}cc@{}}
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\begin{tabular}{@{}p{5.2cm}}
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\includegraphics[scale=0.058]{../pics/towerbridge.jpg}\\
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{\bf bridges}: \\
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\raggedright\small |
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engineers can ``look'' at a bridge and have a pretty good |
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intuition about whether it will hold up or not\\ |
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(redundancy; predictive theory) |
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\end{tabular} &
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\begin{tabular}{p{5cm}}
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\includegraphics[scale=0.265]{../pics/code.jpg}\\
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\raggedright |
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{\bf code}: \\
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\raggedright\small |
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programmers have very little intuition about their code; |
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often it is too expensive to have redundancy; |
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not ``continuous'' |
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\end{tabular}
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\end{tabular}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Dijkstra on Testing}
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\begin{bubble}[10cm]
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``Program testing can be a very effective way to show the |
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presence of bugs, but it is hopelessly inadequate for showing |
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their absence.'' |
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\end{bubble}\bigskip
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{\Large Proving Programs to be Correct}
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\begin{bubble}[10cm]
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\small |
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{\bf Theorem:} There are infinitely many prime
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numbers.\medskip\\ |
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{\bf Proof} \ldots\\
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\end{bubble}\bigskip
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similarly\bigskip |
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\begin{bubble}[10cm]
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\small |
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{\bf Theorem:} The program is doing what
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it is supposed to be doing.\medskip |
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{\bf Long, long proof} \ldots\\
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\end{bubble}\bigskip\medskip
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\small This can be a gigantic proof. The only hope is to have |
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help from the computer. `Program' is here to be understood to be |
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quite general (protocols, OS, \ldots). |
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{\Large{}Mars Pathfinder Mission 1997}
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\begin{center}
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\includegraphics[scale=0.15]{../pics/marspath1.png}
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\includegraphics[scale=0.16]{../pics/marspath3.png}
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\includegraphics[scale=0.3]{../pics/marsrover.png}
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\end{center}
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\begin{itemize}
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\item despite NASA's famous testing procedures, the lander crashed frequently on Mars |
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\item a scheduling algorithm was not used in the OS |
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\begin{textblock}{11}(1,3)
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\begin{tabular}{@{\hspace{-10mm}}l}
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\begin{tikzpicture}[scale=1.1]
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\node at (-2.5,-1.5) {\textcolor{white}{a}};
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\node at (8,4) {\textcolor{white}{a}};
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\only<1>{
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\draw[fill, blue!50] (1,0) rectangle (3,0.6); |
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} |
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\only<2>{
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\draw[fill, blue!50] (1,0) rectangle (2,0.6); |
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\draw[fill, blue!50] (3,0) rectangle (5,0.6); |
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\draw[fill, blue!100] (2,3) rectangle (3,3.6); |
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} |
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\only<3>{
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\draw[fill, blue!50] (1,0) rectangle (2,0.6); |
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\draw[fill, blue!50] (3,0) rectangle (4.5,0.6); |
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\draw[fill, blue!50] (5.5,0) rectangle (6,0.6); |
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\draw[fill, blue!100] (2,3) rectangle (3,3.6); |
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\draw[fill, blue!100] (4.5,3) rectangle (5.5,3.6); |
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} |
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\only<4>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2,0.6); |
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\draw[blue!50, very thick] (2,0) rectangle (4,0.6); |
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\draw[blue!100, very thick] (2,3) rectangle (3, 3.6); |
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\draw[red, <-, line width = 2mm] (2,-0.1) -- (2, -1); |
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} |
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\only<5>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (4,0.6); |
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\draw[blue!100, fill] (4,3) rectangle (5, 3.6); |
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} |
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\only<6>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2,0.6); |
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\draw[blue!50, very thick] (2,0) rectangle (4,0.6); |
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\draw[blue!100, very thick] (2,3) rectangle (3, 3.6); |
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\draw[red, <-, line width = 2mm] (2,-0.1) -- (2, -1); |
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} |
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\only<7>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2.5,0.6); |
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\draw[blue!50, very thick] (2.5,0) rectangle (4,0.6); |
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\draw[blue!100, very thick] (2.5,3) rectangle (3.5, 3.6); |
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\draw[red, <-, line width = 2mm] (2.5,-0.1) -- (2.5, -1); |
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} |
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\only<8>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2.5,0.6); |
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\draw[blue!50, very thick] (2.5,0) rectangle (4,0.6); |
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\draw[blue!100, very thick] (2.5,3) rectangle (3.5, 3.6); |
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\draw[blue!100, very thick] (2.5,3) rectangle (3.5, 3.6); |
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\draw[red, fill] (2.5,1.5) rectangle (3.5,2.1); |
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\draw[red, <-, line width = 2mm] (2.5,-0.1) -- (2.5, -1); |
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} |
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\only<9>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2.5,0.6); |
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\draw[blue!50, very thick] (3.5,0) rectangle (5,0.6); |
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\draw[blue!100, very thick] (3.5,3) rectangle (4.5, 3.6); |
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\draw[red, fill] (2.5,1.5) rectangle (3.5,2.1); |
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\draw[red, <-, line width = 2mm] (3.5,-0.1) -- (3.5, -1); |
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} |
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\only<10>{
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\node at (2.5,0.9) {\small locked a resource};
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\draw[fill, blue!50] (1,0) rectangle (2.5,0.6); |
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\draw[blue!50, very thick] (3.5,0) rectangle (5,0.6); |
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\draw[blue!100, very thick] (3.5,3) rectangle (4.5, 3.6); |
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\draw[red, fill] (2.5,1.5) rectangle (3.5,2.1); |
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\draw[red, fill] (3.55,1.5) rectangle (4.5,2.1); |
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\draw[red, <-, line width = 2mm] (3.5,-0.1) -- (3.5, -1); |
|
215 |
} |
|
216 |
\only<11>{
|
|
217 |
\node at (2.5,0.9) {\small locked a resource};
|
|
218 |
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|
219 |
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|
220 |
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|
221 |
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|
222 |
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|
223 |
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|
224 |
} |
|
225 |
\only<12>{
|
|
226 |
\node at (2.5,0.9) {\small locked a resource};
|
|
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|
228 |
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|
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|
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|
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|
232 |
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|
233 |
\draw[red, <-, line width = 2mm] (5.5,-0.1) -- (5.5, -1); |
|
234 |
\node [anchor=base] at (6.3, 1.8) {\Large\ldots};
|
|
235 |
} |
|
236 |
\only<13>{
|
|
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\node at (2.5,0.9) {\small locked a resource};
|
|
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|
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\draw[blue!50, very thick] (2,0) rectangle (4,0.6); |
|
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|
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|
242 |
} |
|
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\only<14>{
|
|
244 |
\node at (2.5,3.9) {\small locked a resource};
|
|
245 |
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|
246 |
\draw[blue!50, fill] (2,3) rectangle (4,3.6); |
|
247 |
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|
248 |
\draw[blue!50, ->, line width = 2mm] (2,1) -- (2, 2.5); |
|
249 |
\draw[red, <-, line width = 2mm] (2,-0.1) -- (2, -1); |
|
250 |
} |
|
251 |
\only<15>{
|
|
252 |
\node at (2.5,3.9) {\small locked a resource};
|
|
253 |
\draw[fill, blue!50] (1,0) rectangle (2,0.6); |
|
254 |
\draw[blue!50, fill] (2,3) rectangle (4,3.6); |
|
255 |
\draw[blue!100, very thick] (4,3) rectangle (5, 3.6); |
|
256 |
\draw[red, <-, line width = 2mm] (2.5,-0.1) -- (2.5, -1); |
|
257 |
\draw[red, very thick] (2.5,1.5) rectangle (3.5,2.1); |
|
258 |
} |
|
259 |
||
260 |
||
261 |
\draw[very thick,->](0,0) -- (8,0); |
|
262 |
\node [anchor=base] at (8, -0.3) {\scriptsize time};
|
|
263 |
\node [anchor=base] at (0, -0.3) {\scriptsize 0};
|
|
264 |
\node [anchor=base] at (-1.2, 0.2) {\small low priority};
|
|
265 |
\only<2->{\node [anchor=base] at (-1.2, 3.2) {\small high priority};}
|
|
266 |
\only<8->{\node [anchor=base] at (-1.5, 1.7) {\small medium pr.};}
|
|
267 |
||
268 |
\end{tikzpicture}
|
|
269 |
\end{tabular}
|
|
270 |
\end{textblock}
|
|
271 |
||
272 |
\begin{textblock}{0}(2.5,13)%
|
|
273 |
\small |
|
274 |
\onslide<3->{
|
|
275 |
\begin{bubble}[8cm]%
|
|
276 |
Scheduling: You want to avoid that a high |
|
277 |
priority process is starved indefinitely. |
|
278 |
\end{bubble}}
|
|
279 |
\end{textblock}
|
|
280 |
||
281 |
\end{frame}
|
|
282 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
283 |
||
284 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
285 |
\begin{frame}[c]
|
|
286 |
\frametitle{\Large Priority Inheritance Scheduling}
|
|
287 |
||
288 |
\begin{itemize}
|
|
289 |
\item Let a low priority process $L$ temporarily inherit |
|
290 |
the high priority of $H$ until $L$ leaves the critical |
|
291 |
section unlocking the resource.\bigskip |
|
292 |
\item Once the resource is unlocked $L$ returns to its original |
|
293 |
priority level. |
|
294 |
\end{itemize}
|
|
295 |
||
296 |
\end{frame}
|
|
297 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
298 |
||
299 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
300 |
\begin{frame}[c]
|
|
301 |
||
302 |
\begin{textblock}{11}(1,3)
|
|
303 |
\begin{tabular}{@{\hspace{-10mm}}l}
|
|
304 |
\begin{tikzpicture}[scale=1.1]
|
|
305 |
\node at (-2.5,-1.5) {\textcolor{white}{a}};
|
|
306 |
\node at (8,4) {\textcolor{white}{a}};
|
|
307 |
||
308 |
\only<1>{
|
|
309 |
\draw[fill, blue!50] (1,0) rectangle (6,0.6); |
|
310 |
\node at (1.5,0.9) {\small $A_L$};
|
|
311 |
\node at (2.0,0.9) {\small $B_L$};
|
|
312 |
\node at (3.5,0.9) {\small $A_R$};
|
|
313 |
\node at (5.7,0.9) {\small $B_R$};
|
|
314 |
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|
315 |
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|
316 |
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|
317 |
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|
318 |
} |
|
319 |
\only<2>{
|
|
320 |
\draw[fill, blue!50] (1,0) rectangle (3,0.6); |
|
321 |
\draw[very thick, blue!50] (3,0) rectangle (6,0.6); |
|
322 |
\node at (1.5,0.9) {\small $A_L$};
|
|
323 |
\node at (2.0,0.9) {\small $B_L$};
|
|
324 |
\node at (3.5,0.9) {\small $A_R$};
|
|
325 |
\node at (5.7,0.9) {\small $B_R$};
|
|
326 |
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|
327 |
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|
328 |
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|
329 |
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|
330 |
} |
|
331 |
\only<3>{
|
|
332 |
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|
333 |
\draw[very thick, blue!50] (3,0) rectangle (6,0.6); |
|
334 |
\node at (1.5,0.9) {\small $A_L$};
|
|
335 |
\node at (2.0,0.9) {\small $B_L$};
|
|
336 |
\node at (3.5,0.9) {\small $A_R$};
|
|
337 |
\node at (5.7,0.9) {\small $B_R$};
|
|
338 |
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|
339 |
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|
340 |
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|
341 |
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|
342 |
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|
343 |
\node at (3.5,3.3) {\small $A$};
|
|
344 |
} |
|
345 |
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|
|
346 |
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|
347 |
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|
348 |
\node at (1.5,0.9) {\small $A_L$};
|
|
349 |
\node at (2.0,0.9) {\small $B_L$};
|
|
350 |
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|
|
351 |
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|
|
352 |
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|
353 |
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|
354 |
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|
355 |
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|
356 |
\draw[very thick,blue!100] (3,3) rectangle (4,3.6); |
|
357 |
\node at (3.5,3.3) {\small $A$};
|
|
358 |
\draw[very thick,blue!100] (4,3) rectangle (5,3.6); |
|
359 |
\node at (4.5,3.3) {\small $B$};
|
|
360 |
} |
|
361 |
\only<5>{
|
|
362 |
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|
363 |
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|
364 |
\node at (1.5,0.9) {\small $A_L$};
|
|
365 |
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|
|
366 |
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|
|
367 |
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|
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368 |
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|
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|
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|
372 |
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|
373 |
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|
|
374 |
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|
375 |
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|
|
376 |
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|
377 |
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|
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|
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|
381 |
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|
382 |
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|
|
383 |
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|
|
384 |
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|
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|
|
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|
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|
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|
390 |
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|
391 |
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|
|
392 |
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|
393 |
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|
|
394 |
} |
|
395 |
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|
|
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|
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|
398 |
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|
399 |
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|
|
400 |
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|
|
401 |
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|
|
402 |
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|
|
403 |
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|
404 |
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|
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|
406 |
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|
407 |
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|
408 |
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|
|
409 |
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|
410 |
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|
|
411 |
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|
412 |
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|
413 |
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|
414 |
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|
|
415 |
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|
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|
417 |
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|
418 |
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|
|
419 |
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|
|
420 |
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|
|
421 |
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|
|
422 |
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|
423 |
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|
424 |
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|
425 |
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|
426 |
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|
427 |
\node at (4,3.3) {\small $A$};
|
|
428 |
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|
429 |
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|
|
430 |
} |
|
431 |
\only<9>{
|
|
432 |
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|
433 |
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|
434 |
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|
435 |
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|
436 |
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|
|
437 |
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|
|
438 |
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|
|
439 |
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|
|
440 |
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|
441 |
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|
442 |
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|
443 |
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|
444 |
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|
445 |
\node at (4,3.3) {\small $A$};
|
|
446 |
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|
447 |
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|
|
448 |
} |
|
449 |
\only<10>{
|
|
450 |
\draw[fill, blue!50] (1,0) rectangle (3,0.6); |
|
451 |
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|
452 |
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|
453 |
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|
454 |
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|
|
455 |
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|
|
456 |
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|
|
457 |
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|
|
458 |
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|
459 |
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|
460 |
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|
461 |
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|
462 |
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|
463 |
\node at (4,3.3) {\small $A$};
|
|
464 |
\draw[very thick,blue!100] (7,3) rectangle (8,3.6); |
|
465 |
\node at (7.5,3.3) {\small $B$};
|
|
466 |
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|
467 |
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|
468 |
} |
|
469 |
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|
|
470 |
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|
471 |
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|
472 |
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|
473 |
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|
474 |
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|
|
475 |
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|
|
476 |
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|
|
477 |
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|
|
478 |
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|
479 |
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|
480 |
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|
481 |
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|
482 |
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|
483 |
\node at (4,3.3) {\small $A$};
|
|
484 |
\draw[very thick,blue!100] (7,3) rectangle (8,3.6); |
|
485 |
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|
|
486 |
\draw[red, fill] (5,1.5) rectangle (6,2.1); |
|
487 |
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|
488 |
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|
489 |
\draw[blue!50, ->, line width = 2mm] (7.1,4) -- (8,4); |
|
490 |
} |
|
491 |
||
492 |
\draw[very thick,->](0,0) -- (8,0); |
|
493 |
\node [anchor=base] at (8, -0.3) {\scriptsize time};
|
|
494 |
\node [anchor=base] at (0, -0.3) {\scriptsize 0};
|
|
495 |
\node [anchor=base] at (-1.2, 0.2) {\small low priority};
|
|
496 |
\only<2->{\node [anchor=base] at (-1.2, 3.2) {\small high priority};}
|
|
497 |
\only<10->{\node [anchor=base] at (-1.5, 1.7) {\small medium pr.};}
|
|
498 |
||
499 |
\end{tikzpicture}
|
|
500 |
\end{tabular}
|
|
501 |
\end{textblock}
|
|
502 |
||
503 |
\begin{textblock}{0}(2.5,13)%
|
|
504 |
\small |
|
505 |
\onslide<11>{
|
|
506 |
\begin{bubble}[8cm]%
|
|
507 |
Scheduling: You want to avoid that a high |
|
508 |
priority process is staved indefinitely. |
|
509 |
\end{bubble}}
|
|
510 |
\end{textblock}
|
|
511 |
||
512 |
||
513 |
\end{frame}
|
|
514 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
515 |
||
516 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
517 |
\begin{frame}[c]
|
|
518 |
\frametitle{\Large Priority Inheritance Scheduling}
|
|
519 |
||
520 |
\begin{itemize}
|
|
521 |
\item Let a low priority process $L$ temporarily inherit |
|
522 |
the high priority of $H$ until $L$ leaves the critical |
|
523 |
section unlocking the resource.\bigskip |
|
524 |
\item Once the resource is unlocked $L$ returns to its original |
|
525 |
priority level. \alert{\bf BOGUS}\pause\bigskip
|
|
526 |
\item \ldots $L$ needs to switch to the highest |
|
527 |
\alert{remaining} priority of the threads that it blocks.
|
|
528 |
\end{itemize}\bigskip
|
|
529 |
||
530 |
\small this error is already known since around 1999 |
|
531 |
||
532 |
\end{frame}
|
|
533 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
534 |
||
535 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
536 |
\begin{frame}[c]
|
|
537 |
||
538 |
\begin{center}
|
|
539 |
\includegraphics[scale=0.25]{../pics/p3.jpg}
|
|
540 |
\end{center}
|
|
541 |
||
542 |
\begin{itemize}
|
|
543 |
\item by Rajkumar, 1991 |
|
544 |
\item \it ``it resumes the priority it had at the point of entry into the critical |
|
545 |
section'' |
|
546 |
\end{itemize}
|
|
547 |
||
548 |
\end{frame}
|
|
549 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
550 |
||
551 |
||
552 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
553 |
\begin{frame}[c]
|
|
554 |
||
555 |
\begin{center}
|
|
556 |
\includegraphics[scale=0.25]{../pics/p2.jpg}
|
|
557 |
\end{center}
|
|
558 |
||
559 |
\begin{itemize}
|
|
560 |
\item by Jane Liu, 2000 |
|
561 |
\item {\it ``The job $J_l$ executes at its inherited
|
|
562 |
priority until it releases $R$; at that time, the |
|
563 |
priority of $J_l$ returns to its priority |
|
564 |
at the time when it acquires the resource $R$.''}\medskip |
|
565 |
\item \small gives pseudo code and totally bogus data structures |
|
566 |
\item \small interesting part ``{\it left as an exercise}''
|
|
567 |
\end{itemize}
|
|
568 |
||
569 |
\end{frame}
|
|
570 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
571 |
||
572 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
573 |
\begin{frame}[c]
|
|
574 |
||
575 |
\begin{center}
|
|
576 |
\includegraphics[scale=0.15]{../pics/p1.pdf}
|
|
577 |
\end{center}
|
|
578 |
||
579 |
\begin{itemize}
|
|
580 |
\item by Laplante and Ovaska, 2011 (\$113.76) |
|
581 |
\item \it ``when $[$the task$]$ exits the critical section that |
|
582 |
caused the block, it reverts to the priority it had |
|
583 |
when it entered that section'' |
|
584 |
\end{itemize}
|
|
585 |
||
586 |
\end{frame}
|
|
587 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
588 |
||
589 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
590 |
\begin{frame}[c]
|
|
591 |
||
592 |
\begin{center}
|
|
593 |
\includegraphics[scale=0.25]{../pics/p4.jpg}
|
|
594 |
\end{center}
|
|
595 |
||
596 |
\begin{itemize}
|
|
597 |
\item by Silberschatz, Galvin, and Gagne, 2013 (OS-bible) |
|
598 |
\item \it ``Upon releasing the lock, the |
|
599 |
$[$low-priority$]$ thread will revert to |
|
600 |
its original priority.'' |
|
601 |
\end{itemize}
|
|
602 |
||
603 |
\end{frame}
|
|
604 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
605 |
||
606 |
||
607 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
608 |
\begin{frame}[c]
|
|
609 |
\frametitle{Priority Scheduling}
|
|
610 |
||
611 |
\begin{itemize}
|
|
612 |
\item a scheduling algorithm that is widely used in real-time operating systems |
|
613 |
\item has been ``proved'' correct by hand in a paper in 1983 |
|
614 |
\item but this algorithm turned out to be incorrect, despite its ``proof''\bigskip\pause |
|
615 |
||
616 |
\item we used the corrected algorithm and then {\bf really} proved
|
|
617 |
that it is correct |
|
618 |
||
619 |
\item we implemented this algorithm in a small OS called PINTOS |
|
620 |
(used for teaching at Stanford) |
|
621 |
||
622 |
\item our implementation was much more efficient than their |
|
623 |
reference implementation |
|
624 |
||
625 |
\end{itemize}
|
|
626 |
||
627 |
\end{frame}
|
|
628 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
629 |
||
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
630 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
631 |
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
632 |
\begin{frame}[c]
|
| 538 | 633 |
\frametitle{Big Proofs in CS (1)}
|
634 |
||
635 |
Formal proofs in CS sound like science fiction? |
|
|
206
85b961f1eee9
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
151
diff
changeset
|
636 |
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
637 |
\begin{itemize}
|
| 538 | 638 |
\item in 2008, verification of a C-compiler |
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
639 |
\begin{itemize}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
640 |
\item ``if my input program has a certain behaviour, then the compiled machine code has the same behaviour'' |
| 538 | 641 |
\item is as good as \texttt{gcc -O1}, but much less buggy
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
642 |
\end{itemize}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
643 |
\end{itemize}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
644 |
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
645 |
\begin{center}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
646 |
\includegraphics[scale=0.12]{../pics/compcert.png}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
647 |
\end{center}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
648 |
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
649 |
\end{frame}
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
650 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
206
85b961f1eee9
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
151
diff
changeset
|
651 |
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
652 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 538 | 653 |
% \begin{frame}[c]
|
654 |
% \frametitle{Fuzzy Testing C-Compilers}
|
|
655 |
||
656 |
% \begin{itemize}
|
|
657 |
% \item tested GCC, LLVM and others by randomly generating |
|
658 |
% C-programs |
|
659 |
% \item found more than 300 bugs in GCC and also |
|
660 |
% many in LLVM (some of them highest-level critical)\bigskip |
|
661 |
% \item about CompCert: |
|
662 |
||
663 |
% \begin{bubble}[10cm]\small ``The striking thing about our CompCert
|
|
664 |
% results is that the middle-end bugs we found in all other |
|
665 |
% compilers are absent. As of early 2011, the under-development |
|
666 |
% version of CompCert is the only compiler we have tested for |
|
667 |
% which Csmith cannot find wrong-code errors. This is not for |
|
668 |
% lack of trying: we have devoted about six CPU-years to the |
|
669 |
% task.'' |
|
670 |
% \end{bubble}
|
|
671 |
% \end{itemize}
|
|
672 |
||
673 |
% \end{frame}
|
|
674 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
675 |
||
676 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
677 |
\begin{frame}[c]
|
| 538 | 678 |
\frametitle{Big Proofs in CS (2)}
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
679 |
|
|
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
680 |
\begin{itemize}
|
| 538 | 681 |
\item in 2010, verification of a micro-kernel operating system (approximately 8700 loc) |
682 |
\begin{itemize}
|
|
683 |
\item used in helicopters and mobile phones |
|
684 |
\item 200k loc of proof |
|
685 |
\item 25 - 30 person years |
|
686 |
\item found 160 bugs in the C code (144 by the proof) |
|
687 |
\end{itemize}
|
|
688 |
\end{itemize}
|
|
689 |
||
690 |
\begin{bubble}[10cm]\small
|
|
691 |
``Real-world operating-system kernel with an end-to-end proof |
|
692 |
of implementation correctness and security enforcement'' |
|
693 |
\end{bubble}\bigskip\pause
|
|
694 |
||
695 |
unhackable kernel (New Scientists, September 2015) |
|
696 |
\end{frame}
|
|
697 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
698 |
||
699 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
700 |
\begin{frame}[c]
|
|
701 |
\frametitle{Big Proofs in CS (3)}
|
|
702 |
||
703 |
\begin{itemize}
|
|
704 |
\item verified TLS implementation\medskip |
|
705 |
\item verified compilers (CompCert, CakeML)\medskip |
|
706 |
\item verified distributed systems (Verdi)\medskip |
|
707 |
\item verified OSes or OS components\\ |
|
708 |
(seL4, CertiKOS, \ldots)\bigskip\pause |
|
709 |
\item Infer static analyser developed by Facebook |
|
710 |
\end{itemize}
|
|
711 |
||
712 |
\end{frame}
|
|
|
206
85b961f1eee9
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
151
diff
changeset
|
713 |
|
| 538 | 714 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
715 |
\begin{frame}[c]
|
|
716 |
\frametitle{How Did This Happen?}
|
|
717 |
||
718 |
Lots of ways! |
|
719 |
||
720 |
\begin{itemize}
|
|
721 |
\item better programming languages |
|
722 |
\begin{itemize}
|
|
723 |
\item basic safety guarantees built in \item powerful mechanisms for abstraction and modularity |
|
724 |
\end{itemize}
|
|
725 |
\item better software development methodology |
|
726 |
\item stable platforms and frameworks |
|
727 |
\item better use of specifications\medskip\\ |
|
728 |
\small If you want to build software that works or is secure, |
|
729 |
it is helpful to know what you mean by ``works'' and by ``is secure''! |
|
730 |
\end{itemize}
|
|
731 |
||
732 |
\end{frame}
|
|
733 |
||
734 |
||
735 |
||
736 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
737 |
\begin{frame}[c]
|
|
738 |
\frametitle{Goal}
|
|
739 |
||
740 |
Remember the Bridges example? |
|
741 |
||
742 |
\begin{itemize}
|
|
743 |
\item Can we look at our programs and somehow ensure |
|
744 |
they are bug free/correct?\pause\bigskip |
|
745 |
||
746 |
\item Very hard: Anything interesting about programs is equivalent |
|
747 |
to the Halting Problem, which is undecidable.\pause\bigskip |
|
748 |
||
749 |
\item \alert{Solution:} We avoid this ``minor'' obstacle by
|
|
750 |
being as close as possible of deciding the halting |
|
751 |
problem, without actually deciding the halting problem. |
|
752 |
\small$\quad\Rightarrow$ yes, no, don't know (static analysis) |
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
753 |
\end{itemize}
|
|
206
85b961f1eee9
added
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
151
diff
changeset
|
754 |
|
|
383
a6a6bf32fade
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
381
diff
changeset
|
755 |
\end{frame}
|
| 538 | 756 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
757 |
||
758 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
759 |
\begin{frame}[c]
|
|
760 |
\frametitle{What is Static Analysis?}
|
|
761 |
||
762 |
\begin{center}
|
|
763 |
\includegraphics[scale=0.4]{../pics/state.png}
|
|
764 |
\end{center}
|
|
765 |
||
766 |
\begin{itemize}
|
|
767 |
\item depending on some initial input, a program |
|
768 |
(behaviour) will ``develop'' over time. |
|
769 |
\end{itemize}
|
|
770 |
||
771 |
\end{frame}
|
|
772 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
773 |
||
774 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
775 |
\begin{frame}[c]
|
|
776 |
\frametitle{What is Static Analysis?}
|
|
777 |
||
778 |
\begin{center}
|
|
779 |
\includegraphics[scale=0.4]{../pics/state2.png}
|
|
780 |
\end{center}
|
|
781 |
||
782 |
\end{frame}
|
|
783 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
784 |
||
785 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
786 |
\begin{frame}[c]
|
|
787 |
\frametitle{What is Static Analysis?}
|
|
788 |
||
789 |
\begin{center}
|
|
790 |
\includegraphics[scale=0.4]{../pics/state3.jpg}
|
|
791 |
\end{center}
|
|
792 |
||
793 |
\end{frame}
|
|
794 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
795 |
||
796 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
797 |
\begin{frame}[c]
|
|
798 |
\frametitle{What is Static Analysis?}
|
|
799 |
||
800 |
\begin{center}
|
|
801 |
\includegraphics[scale=0.4]{../pics/state4.jpg}
|
|
802 |
\end{center}
|
|
803 |
||
804 |
\begin{itemize}
|
|
805 |
\item to be avoided |
|
806 |
\end{itemize}
|
|
807 |
||
808 |
\end{frame}
|
|
809 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
810 |
||
811 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
812 |
\begin{frame}[c]
|
|
813 |
\frametitle{What is Static Analysis?}
|
|
814 |
||
815 |
\begin{center}
|
|
816 |
\includegraphics[scale=0.4]{../pics/state5.png}
|
|
817 |
\end{center}
|
|
818 |
||
819 |
\begin{itemize}
|
|
820 |
\item this needs more work |
|
821 |
\end{itemize}
|
|
822 |
||
823 |
\end{frame}
|
|
824 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
825 |
||
826 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
827 |
\begin{frame}[c]
|
|
828 |
\frametitle{What is Static Analysis?}
|
|
829 |
||
830 |
\begin{center}
|
|
831 |
\includegraphics[scale=0.4]{../pics/state6.png}
|
|
832 |
\end{center}
|
|
833 |
||
834 |
\end{frame}
|
|
835 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
836 |
||
837 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
838 |
\begin{frame}[c,fragile]
|
|
839 |
\frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
840 |
Are Vars Definitely Initialised?\end{tabular}}
|
|
841 |
||
842 |
Assuming \texttt{x} is initialised, what about \texttt{y}?\bigskip
|
|
843 |
||
844 |
Prog.~1:\\ |
|
845 |
\begin{lstlisting}[numbers=none,
|
|
846 |
basicstyle=\ttfamily, |
|
847 |
language=While,xleftmargin=3mm] |
|
848 |
if x < 1 then y := x else y := x + 1; |
|
849 |
y := y + 1 |
|
850 |
\end{lstlisting}\medskip
|
|
851 |
||
852 |
Prog.~2:\\ |
|
853 |
\begin{lstlisting}[numbers=none,
|
|
854 |
basicstyle=\ttfamily, |
|
855 |
language=While,xleftmargin=3mm] |
|
856 |
if x < x then y := y + 1 else y := x; |
|
857 |
y := y + 1 |
|
858 |
\end{lstlisting}
|
|
859 |
||
860 |
\end{frame}
|
|
861 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
862 |
||
863 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
864 |
\begin{frame}[c,fragile]
|
|
865 |
\frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
866 |
Are Vars Definitely Initialised?\end{tabular}}
|
|
867 |
||
868 |
What should the rules be for deciding when a |
|
869 |
variable is initialised?\bigskip\pause |
|
870 |
||
871 |
\begin{itemize}
|
|
872 |
\item variable \texttt{x} is definitely initialized after
|
|
873 |
\texttt{skip}\\
|
|
874 |
iff \texttt{x} is definitely initialized before \texttt{skip}.
|
|
875 |
\end{itemize}
|
|
876 |
||
877 |
\end{frame}
|
|
878 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
879 |
||
880 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
881 |
\begin{frame}[c,fragile]
|
|
882 |
% \frametitle{\Large\begin{tabular}{c}Concrete Example:\\[-1mm]
|
|
883 |
% Are Vars Definitely Initialised?\end{tabular}}
|
|
884 |
||
885 |
$\bl{A}$ is the set of definitely defined variables:
|
|
886 |
||
887 |
\begin{center}
|
|
888 |
\begin{tabular}{c}
|
|
889 |
\bl{\infer{\mbox{}}{A\;\texttt{skip}\;A}}\qquad
|
|
890 |
\bl{\infer{vars(a) \subseteq A}{A\;\;(\texttt{x\,:=\,a})\;\;\{x\}\cup A}}
|
|
891 |
\medskip\\\pause |
|
892 |
||
893 |
\bl{\infer{A_1\;s_1\;A_2\quad A_2\;s_2\;A_3}{A_1\;(s_1 ; s_2)\;A_3}}
|
|
894 |
\medskip\\\pause |
|
895 |
||
896 |
\bl{\infer{vars(b)\subseteq A\quad A\;s_1\;A_1\quad A\;s_2\;A_2}
|
|
897 |
{A\;(\texttt{if}\;b\;\texttt{then}\;s_1\;\texttt{else}\;s_2)\;A_1\cap A_2}}
|
|
898 |
\medskip\\\pause |
|
899 |
||
900 |
\bl{\infer{vars(b)\subseteq A\quad A\;s\;A'}
|
|
901 |
{A\;(\texttt{while}\;b\;\texttt{do}\;s)\;A}}\pause
|
|
902 |
\end{tabular}
|
|
903 |
\end{center}
|
|
904 |
||
905 |
\hfill we start with $\bl{A = \{\}}$
|
|
906 |
\end{frame}
|
|
907 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
908 |
||
909 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
910 |
\begin{frame}[fragile]
|
|
911 |
\frametitle{\large Concrete Example: Sign-Analysis}
|
|
912 |
\mbox{}\\[-20mm]\mbox{}
|
|
913 |
||
914 |
\bl{\begin{plstx}[rhs style=,one per line]
: \meta{Exp} ::= \meta{Exp} + \meta{Exp}
|
|
915 |
| \meta{Exp} * \meta{Exp}
|
|
916 |
| \meta{Exp} = \meta{Exp}
|
|
917 |
| \meta{num}
|
|
918 |
| \meta{var}\\
|
|
919 |
: \meta{Stmt} ::= \meta{label} :
|
|
920 |
| \meta{var} := \meta{Exp}
|
|
921 |
| \pcode{jmp?} \meta{Exp} \meta{label}
|
|
922 |
| \pcode{goto} \meta{label}\\
|
|
923 |
: \meta{Prog} ::= \meta{Stmt} \ldots{} \meta{Stmt}\\
|
|
924 |
\end{plstx}}
|
|
925 |
||
926 |
\begin{textblock}{0}(7.8,2.5)
|
|
927 |
\small |
|
928 |
\begin{bubble}[5.6cm]
|
|
929 |
\begin{lstlisting}[numbers=none,
|
|
930 |
basicstyle=\ttfamily, |
|
931 |
language={},xleftmargin=3mm]
|
|
932 |
a := 1 |
|
933 |
n := 5 |
|
934 |
top: jmp? n = 0 done |
|
935 |
a := a * n |
|
936 |
n := n + -1 |
|
937 |
goto top |
|
938 |
done: |
|
939 |
\end{lstlisting}
|
|
940 |
\end{bubble}
|
|
941 |
\end{textblock}
|
|
942 |
||
943 |
\end{frame}
|
|
944 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
945 |
||
946 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
947 |
\begin{frame}[fragile]
|
|
948 |
\frametitle{\large Concrete Example: Sign-Analysis}
|
|
949 |
\mbox{}\\[-20mm]\mbox{}
|
|
950 |
||
951 |
\bl{\begin{plstx}[rhs style=,one per line]
: \meta{Exp} ::= \meta{Exp} + \meta{Exp}
|
|
952 |
| \meta{Exp} * \meta{Exp}
|
|
953 |
| \meta{Exp} = \meta{Exp}
|
|
954 |
| \meta{num}
|
|
955 |
| \meta{var}\\
|
|
956 |
: \meta{Stmt} ::= \meta{label} :
|
|
957 |
| \meta{var} := \meta{Exp}
|
|
958 |
| \pcode{jmp?} \meta{Exp} \meta{label}
|
|
959 |
| \pcode{goto} \meta{label}\\
|
|
960 |
: \meta{Prog} ::= \meta{Stmt} \ldots{} \meta{Stmt}\\
|
|
961 |
\end{plstx}}
|
|
962 |
||
963 |
\begin{textblock}{0}(7.8,3.5)
|
|
964 |
\small |
|
965 |
\begin{bubble}[5.6cm]
|
|
966 |
\begin{lstlisting}[numbers=none,
|
|
967 |
basicstyle=\ttfamily, |
|
968 |
language={},xleftmargin=3mm]
|
|
969 |
n := 6 |
|
970 |
m1 := 0 |
|
971 |
m2 := 1 |
|
972 |
top: jmp? n = 0 done |
|
973 |
tmp := m2 |
|
974 |
m2 := m1 + m2 |
|
975 |
m1 := tmp |
|
976 |
n := n + -1 |
|
977 |
goto top |
|
978 |
done: |
|
979 |
\end{lstlisting}
|
|
980 |
\end{bubble}
|
|
981 |
\end{textblock}
|
|
982 |
||
983 |
\end{frame}
|
|
984 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
985 |
||
986 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
987 |
\begin{frame}[fragile]
|
|
988 |
\frametitle{\large Concrete Example: Sign-Analysis}
|
|
989 |
\mbox{}\\[-20mm]\mbox{}
|
|
990 |
||
991 |
\bl{\begin{plstx}[rhs style=,one per line]
: \meta{Exp} ::= \meta{Exp} + \meta{Exp}
|
|
992 |
| \meta{Exp} * \meta{Exp}
|
|
993 |
| \meta{Exp} = \meta{Exp}
|
|
994 |
| \meta{num}
|
|
995 |
| \meta{var}\\
|
|
996 |
: \meta{Stmt} ::= \meta{label} :
|
|
997 |
| \meta{var} := \meta{Exp}
|
|
998 |
| \pcode{jmp?} \meta{Exp} \meta{label}
|
|
999 |
| \pcode{goto} \meta{label}\\
|
|
1000 |
: \meta{Prog} ::= \meta{Stmt} \ldots{} \meta{Stmt}\\
|
|
1001 |
\end{plstx}}
|
|
1002 |
||
1003 |
\end{frame}
|
|
1004 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1005 |
||
1006 |
||
1007 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1008 |
\begin{frame}[fragile]
|
|
1009 |
\frametitle{Eval: An Interpreter}
|
|
1010 |
\mbox{}\\[-14mm]\mbox{}
|
|
1011 |
||
1012 |
\small |
|
1013 |
\begin{center}
|
|
1014 |
\bl{\begin{tabular}{lcl}
|
|
1015 |
$[n]_{env}$ & $\dn$ & $n$\\
|
|
1016 |
$[x]_{env}$ & $\dn$ & $env(x)$\\
|
|
1017 |
$[e_1 + e_2]_{env}$ & $\dn$ & $[e_1]_{env} + [e_2]_{env}$\\
|
|
1018 |
$[e_1 * e_2]_{env}$ & $\dn$ & $[e_1]_{env} * [e_2]_{env}$\\
|
|
1019 |
$[e_1 = e_2]_{env}$ & $\dn$ &
|
|
1020 |
$\begin{cases}
|
|
1021 |
1 & \text{if}\quad[e_1]_{env} = [e_2]_{env}\\
|
|
1022 |
0 & \text{otherwise}
|
|
1023 |
\end{cases}$\\
|
|
1024 |
\end{tabular}}
|
|
1025 |
\end{center}
|
|
1026 |
||
1027 |
\footnotesize |
|
1028 |
\begin{lstlisting}[numbers=none,xleftmargin=-5mm]
|
|
1029 |
def eval_exp(e: Exp, env: Env) : Int = e match {
|
|
1030 |
case Num(n) => n |
|
1031 |
case Var(x) => env(x) |
|
1032 |
case Plus(e1, e2) => eval_exp(e1, env) + eval_exp(e2, env) |
|
1033 |
case Times(e1, e2) => eval_exp(e1, env) * eval_exp(e2, env) |
|
1034 |
case Equ(e1, e2) => |
|
1035 |
if (eval_exp(e1, env) == eval_exp(e2, env)) 1 else 0 |
|
1036 |
} |
|
1037 |
\end{lstlisting}
|
|
1038 |
||
1039 |
\end{frame}
|
|
1040 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1041 |
||
1042 |
||
1043 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1044 |
\begin{frame}[fragile]
|
|
1045 |
\small |
|
1046 |
A program |
|
1047 |
\begin{bubble}[6cm]\footnotesize
|
|
1048 |
\begin{lstlisting}[numbers=none,
|
|
1049 |
language={},
|
|
1050 |
basicstyle=\ttfamily, |
|
1051 |
xleftmargin=1mm] |
|
1052 |
a := 1 |
|
1053 |
n := 5 |
|
1054 |
top: jmp? n = 0 done |
|
1055 |
a := a * n |
|
1056 |
n := n + -1 |
|
1057 |
goto top |
|
1058 |
done: |
|
1059 |
\end{lstlisting}
|
|
1060 |
\end{bubble}
|
|
1061 |
||
1062 |
The \emph{snippets} of the program:
|
|
1063 |
||
1064 |
\footnotesize |
|
1065 |
\begin{columns}
|
|
1066 |
\begin{column}[t]{5cm}
|
|
1067 |
\begin{bubble}[4.5cm]
|
|
1068 |
\begin{lstlisting}[numbers=none,
|
|
1069 |
basicstyle=\ttfamily, |
|
1070 |
language={},xleftmargin=1mm]
|
|
1071 |
"" a := 1 |
|
1072 |
n := 5 |
|
1073 |
top: jmp? n = 0 done |
|
1074 |
a := a * n |
|
1075 |
n := n + -1 |
|
1076 |
goto top |
|
1077 |
done: |
|
1078 |
\end{lstlisting}
|
|
1079 |
\end{bubble}
|
|
1080 |
\end{column}
|
|
1081 |
\begin{column}[t]{5cm}
|
|
1082 |
\begin{bubble}[4.5cm]
|
|
1083 |
\begin{lstlisting}[numbers=none,
|
|
1084 |
basicstyle=\ttfamily, |
|
1085 |
language={},xleftmargin=1mm]
|
|
1086 |
top: jmp? n = 0 done |
|
1087 |
a := a * n |
|
1088 |
n := n + -1 |
|
1089 |
goto top |
|
1090 |
done: |
|
1091 |
\end{lstlisting}
|
|
1092 |
\end{bubble}
|
|
1093 |
\end{column}
|
|
1094 |
\begin{column}[t]{2cm}
|
|
1095 |
\begin{bubble}[1.1cm]
|
|
1096 |
\begin{lstlisting}[numbers=none,
|
|
1097 |
basicstyle=\ttfamily, |
|
1098 |
language={},xleftmargin=1mm]
|
|
1099 |
done: |
|
1100 |
\end{lstlisting}
|
|
1101 |
\end{bubble}
|
|
1102 |
\end{column}
|
|
1103 |
\end{columns}
|
|
1104 |
||
1105 |
\end{frame}
|
|
1106 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1107 |
||
1108 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1109 |
\begin{frame}[fragile]
|
|
1110 |
\frametitle{Eval for Stmts}
|
|
1111 |
\mbox{}\\[-12mm]\mbox{}
|
|
1112 |
||
1113 |
Let \bl{$sn$} be the snippets of a program
|
|
1114 |
||
1115 |
\small |
|
1116 |
\begin{center}
|
|
1117 |
\bl{\begin{tabular}{lcl}
|
|
1118 |
$[\texttt{nil}]_{env}$ & $\dn$ & $env$\medskip\\
|
|
1119 |
$[\texttt{Label}(l:)::rest]_{env}$ & $\dn$ & $[rest]_{env}$\medskip\\
|
|
1120 |
$[x \,\texttt{:=}\, a::rest]_{env}$ & $\dn$ &
|
|
1121 |
$[rest]_{(env[x:= [a]_{env}])}$\medskip\\
|
|
1122 |
$[\texttt{jmp?}\;b\;l::rest]_{env}$ & $\dn$ &
|
|
1123 |
$\begin{cases}
|
|
1124 |
[sn(l)]_{env} & \text{if}\quad[b]_{env} = true\\
|
|
1125 |
[rest]_{env} & \text{otherwise}
|
|
1126 |
\end{cases}$\medskip\\
|
|
1127 |
$[\texttt{goto}\;l::rest]_{env}$ & $\dn$ & $[sn(l)]_{env}$\\
|
|
1128 |
\end{tabular}}
|
|
1129 |
\end{center}\bigskip
|
|
1130 |
||
1131 |
Start with \bl{$[sn(\mbox{\code{""}})]_{\varnothing}$}
|
|
1132 |
||
1133 |
\end{frame}
|
|
1134 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1135 |
||
1136 |
||
1137 |
||
1138 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1139 |
\begin{frame}[fragile]
|
|
1140 |
\frametitle{Eval in Code}
|
|
1141 |
||
1142 |
\footnotesize |
|
1143 |
\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-5mm]
|
|
1144 |
def eval(sn: Snips) : Env = {
|
|
1145 |
def eval_stmts(sts: Stmts, env: Env) : Env = sts match {
|
|
1146 |
case Nil => env |
|
1147 |
||
1148 |
case Label(l)::rest => eval_stmts(rest, env) |
|
1149 |
||
1150 |
case Assign(x, e)::rest => |
|
1151 |
eval_stmts(rest, env + (x -> eval_exp(e, env))) |
|
1152 |
||
1153 |
case Jmp(b, l)::rest => |
|
1154 |
if (eval_exp(b, env) == 1) eval_stmts(sn(l), env) |
|
1155 |
else eval_stmts(rest, env) |
|
1156 |
||
1157 |
case Goto(l)::rest => eval_stmts(sn(l), env) |
|
1158 |
} |
|
1159 |
||
1160 |
eval_stmts(sn(""), Map())
|
|
1161 |
} |
|
1162 |
\end{lstlisting}
|
|
1163 |
||
1164 |
\end{frame}
|
|
1165 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1166 |
||
1167 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1168 |
\begin{frame}[fragile]
|
|
1169 |
\frametitle{The Idea of Static Analysis}
|
|
1170 |
\small |
|
1171 |
\mbox{}\bigskip\\
|
|
1172 |
||
1173 |
\begin{columns}
|
|
1174 |
\begin{column}{5cm}
|
|
1175 |
\begin{bubble}[4.5cm]\footnotesize
|
|
1176 |
\begin{lstlisting}[numbers=none,
|
|
1177 |
language={},
|
|
1178 |
basicstyle=\ttfamily, |
|
1179 |
xleftmargin=1mm] |
|
1180 |
a := 1 |
|
1181 |
n := 5 |
|
1182 |
top: jmp? n = 0 done |
|
1183 |
a := a * n |
|
1184 |
n := n + -1 |
|
1185 |
goto top |
|
1186 |
done: |
|
1187 |
\end{lstlisting}
|
|
1188 |
\end{bubble}
|
|
1189 |
\end{column}
|
|
1190 |
||
1191 |
\begin{column}{1cm}
|
|
1192 |
\raisebox{-20mm}{\LARGE\bf$\Rightarrow$}
|
|
1193 |
\end{column}
|
|
1194 |
\begin{column}{6cm}
|
|
1195 |
\begin{bubble}[4.7cm]\footnotesize
|
|
1196 |
\begin{lstlisting}[numbers=none,
|
|
1197 |
language={},
|
|
1198 |
basicstyle=\ttfamily, |
|
1199 |
xleftmargin=1mm, |
|
1200 |
escapeinside={(*}{*)}]
|
|
1201 |
a := (*\hl{'+'}*)
|
|
1202 |
n := (*\hl{'+'}*)
|
|
1203 |
top: jmp? n = (*\hl{'0'}*) done
|
|
1204 |
a := a * n |
|
1205 |
n := n + (*\hl{'-'}*)
|
|
1206 |
goto top |
|
1207 |
done: |
|
1208 |
\end{lstlisting}
|
|
1209 |
\end{bubble}
|
|
1210 |
\end{column}
|
|
1211 |
\end{columns}\bigskip\bigskip
|
|
1212 |
||
1213 |
Replace all constants and variables by either |
|
1214 |
\pcode{+}, \pcode{-} or \pcode{0}. What we want to find out
|
|
1215 |
is what the sign of \texttt{a} and \texttt{n} is (they should
|
|
1216 |
always positive). |
|
1217 |
||
1218 |
\end{frame}
|
|
1219 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1220 |
||
1221 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1222 |
\begin{frame}[c]
|
|
1223 |
\frametitle{Sign Analysis?}
|
|
1224 |
||
1225 |
||
1226 |
\begin{columns}
|
|
1227 |
\begin{column}{3cm}
|
|
1228 |
\begin{tabular}{cc|l}
|
|
1229 |
$e_1$ & $e_2$ & $e_1 + e_2$\\\hline{}
|
|
1230 |
- & - & -\\ |
|
1231 |
- & 0 & -\\ |
|
1232 |
- & + & -, 0, +\\ |
|
1233 |
0 & $x$ & $x$\\ |
|
1234 |
+ & - & -, 0, +\\ |
|
1235 |
+ & 0 & +\\ |
|
1236 |
+ & + & +\\ |
|
1237 |
\end{tabular}
|
|
1238 |
\end{column}
|
|
1239 |
||
1240 |
\begin{column}{3cm}
|
|
1241 |
\begin{tabular}{cc|l}
|
|
1242 |
$e_1$ & $e_2$ & $e_1 * e_2$\\\hline{}
|
|
1243 |
- & - & +\\ |
|
1244 |
- & 0 & 0\\ |
|
1245 |
- & + & -\\ |
|
1246 |
0 & $x$ & 0\\ |
|
1247 |
+ & - & -\\ |
|
1248 |
+ & 0 & 0\\ |
|
1249 |
+ & + & +\\ |
|
1250 |
\end{tabular}
|
|
1251 |
\end{column}
|
|
1252 |
\end{columns}
|
|
1253 |
||
1254 |
\end{frame}
|
|
1255 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1256 |
||
1257 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1258 |
\begin{frame}[fragile]
|
|
1259 |
\mbox{}\\[-13mm]\mbox{}
|
|
1260 |
||
1261 |
\small |
|
1262 |
\begin{center}
|
|
1263 |
\bl{\begin{tabular}{lcl}
|
|
1264 |
$[n]_{aenv}$ & $\dn$ &
|
|
1265 |
$\begin{cases}
|
|
1266 |
\{+\} & \text{if}\; n > 0\\
|
|
1267 |
\{-\} & \text{if}\; n < 0\\
|
|
1268 |
\{0\} & \text{if}\; n = 0
|
|
1269 |
\end{cases}$\\
|
|
1270 |
$[x]_{aenv}$ & $\dn$ & $aenv(x)$\\
|
|
1271 |
$[e_1 + e_2]_{aenv}$ & $\dn$ & $[e_1]_{aenv} \oplus [e_2]_{aenv}$\\
|
|
1272 |
$[e_1 * e_2]_{aenv}$ & $\dn$ & $[e_1]_{aenv} \otimes [e_2]_{aenv}$\\
|
|
1273 |
$[e_1 = e_2]_{aenv}$ & $\dn$ & $\{0, +\}$\\
|
|
1274 |
\end{tabular}}
|
|
1275 |
\end{center}
|
|
1276 |
||
1277 |
\scriptsize |
|
1278 |
\begin{lstlisting}[language=Scala,numbers=none,xleftmargin=-5mm]
|
|
1279 |
def aeval_exp(e: Exp, aenv: AEnv) : Set[Abst] = e match {
|
|
1280 |
case Num(0) => Set(Zero) |
|
1281 |
case Num(n) if (n < 0) => Set(Neg) |
|
1282 |
case Num(n) if (n > 0) => Set(Pos) |
|
1283 |
case Var(x) => aenv(x) |
|
1284 |
case Plus(e1, e2) => |
|
1285 |
aplus(aeval_exp(e1, aenv), aeval_exp(e2, aenv)) |
|
1286 |
case Times(e1, e2) => |
|
1287 |
atimes(aeval_exp(e1, aenv), aeval_exp(e2, aenv)) |
|
1288 |
case Equ(e1, e2) => Set(Zero, Pos) |
|
1289 |
} |
|
1290 |
\end{lstlisting}
|
|
1291 |
||
1292 |
\end{frame}
|
|
1293 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1294 |
||
1295 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1296 |
\begin{frame}[fragile]
|
|
1297 |
\frametitle{AEval for Stmts}
|
|
1298 |
\mbox{}\\[-12mm]\mbox{}
|
|
1299 |
||
1300 |
Let \bl{$sn$} be the snippets of a program
|
|
1301 |
||
1302 |
\small |
|
1303 |
\begin{center}
|
|
1304 |
\bl{\begin{tabular}{lcl}
|
|
1305 |
$[\texttt{nil}]_{aenv}$ & $\to$ & $(\texttt{nil},aenv)$\medskip\\
|
|
1306 |
$[\texttt{Label}(l:)::rest]_{aenv}$ & $\to$ & $(rest, aenv)$\medskip\\
|
|
1307 |
$[x \,\texttt{:=}\, e::rest]_{aenv}$ & $\to$ &
|
|
1308 |
$(rest, aenv[x:= [e]_{aenv}])$\medskip\\
|
|
1309 |
$[\texttt{jmp?}\;e\;l::rest]_{aenv}$ & $\to$ &
|
|
1310 |
$(sn(l),aenv)$ \textcolor{black}{and} $(rest, aenv)$\medskip\\
|
|
1311 |
$[\texttt{goto}\;l::rest]_{aenv}$ & $\to$ & $(sn(l), aenv)$\\
|
|
1312 |
\end{tabular}}
|
|
1313 |
\end{center}\bigskip
|
|
1314 |
||
1315 |
Start with \bl{$[sn(\mbox{\code{""}})]_{\varnothing}$}, try to
|
|
1316 |
reach all \emph{states} you can find (until a fix point is reached).
|
|
1317 |
||
1318 |
Check whether there are only $aenv$ in the final states that have |
|
1319 |
your property. |
|
1320 |
\end{frame}
|
|
1321 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1322 |
||
1323 |
||
1324 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1325 |
\begin{frame}[c]
|
|
1326 |
\frametitle{Sign Analysis}
|
|
1327 |
||
1328 |
\begin{itemize}
|
|
1329 |
\item We want to find out whether \texttt{a} and \texttt{n}
|
|
1330 |
are always positive?\medskip |
|
1331 |
\item After a few optimisations, we can indeed find this out. |
|
1332 |
\begin{itemize}
|
|
1333 |
\item equal signs return only \texttt{+} or \texttt{0}
|
|
1334 |
\item branch into only one direction if you know |
|
1335 |
\item if $x$ is \texttt{+}, then $x + \texttt{-1}$
|
|
1336 |
cannot be negative |
|
1337 |
\end{itemize}\bigskip
|
|
1338 |
||
1339 |
\item What is this good for? Well, you do not need |
|
1340 |
underflow checks (in order to prevent buffer-overflow |
|
1341 |
attacks). In general this technique is used to make sure |
|
1342 |
keys stay secret. |
|
1343 |
\end{itemize}
|
|
1344 |
||
1345 |
\end{frame}
|
|
1346 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1347 |
||
1348 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1349 |
\begin{frame}[c]
|
|
1350 |
\frametitle{Take Home Points}
|
|
1351 |
||
1352 |
\begin{itemize}
|
|
1353 |
\item While testing is important, it does not show the |
|
1354 |
absence of bugs/vulnerabilities.\medskip |
|
1355 |
\item More and more we need (formal) proofs that show |
|
1356 |
a program is bug free.\medskip |
|
1357 |
||
1358 |
\item Static analysis is more and more employed nowadays |
|
1359 |
in order to automatically hunt for bugs. |
|
1360 |
\end{itemize}
|
|
1361 |
||
1362 |
\end{frame}
|
|
1363 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1364 |
||
1365 |
||
|
82
06c3ec0b452e
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
81
diff
changeset
|
1366 |
|
|
65
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1367 |
\end{document}
|
|
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1368 |
|
| 538 | 1369 |
|
|
65
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1370 |
%%% Local Variables: |
|
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1371 |
%%% mode: latex |
|
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1372 |
%%% TeX-master: t |
|
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1373 |
%%% End: |
|
ade6af51402c
tuned
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
1374 |