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\documentclass[dvipsnames,14pt,t,xelatex]{beamer}
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\usepackage{./slides}
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\usepackage{./graph}
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\usepackage{./langs}
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\usepackage{./data}
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\usepackage{changepage}
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\hfuzz=220pt
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\lstset{language=Scala,
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style=mystyle,
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numbersep=0pt,
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numbers=none,
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xleftmargin=0mm}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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% beamer stuff
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\renewcommand{\slidecaption}{CFL 01, King's College London}
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\begin{filecontents}{re-python2.data}
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1 0.033
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5 0.036
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10 0.034
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15 0.036
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18 0.059
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19 0.084
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20 0.141
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21 0.248
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22 0.485
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23 0.878
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24 1.71
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25 3.40
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26 7.08
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27 14.12
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28 26.69
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\end{filecontents}
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\begin{filecontents}{re-java.data}
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5 0.00298
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10 0.00418
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15 0.00996
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16 0.01710
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17 0.03492
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18 0.03303
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19 0.05084
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20 0.10177
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21 0.19960
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22 0.41159
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23 0.82234
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24 1.70251
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25 3.36112
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26 6.63998
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27 13.35120
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28 29.81185
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\end{filecontents}
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\begin{filecontents}{re-java9.data}
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1000 0.01410
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2000 0.04882
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3000 0.10609
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4000 0.17456
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5000 0.27530
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6000 0.41116
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7000 0.53741
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8000 0.70261
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9000 0.93981
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10000 0.97419
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11000 1.28697
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12000 1.51387
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14000 2.07079
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16000 2.69846
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20000 4.41823
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24000 6.46077
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26000 7.64373
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30000 9.99446
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34000 12.966885
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38000 16.281621
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42000 19.180228
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46000 21.984721
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50000 26.950203
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60000 43.0327746
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\end{filecontents}
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\begin{filecontents}{re-usize.data}
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1 16
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2 33
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3 63
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4 108
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5 181
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6 297
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7 484
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8 785
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9 1271
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10 2056
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11 3325
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12 5377
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13 8696
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14 14065
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15 22751
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16 36804
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17 59541
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18 96329
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19 155852
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20 252161
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21 407991
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22 660128
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23 1068093
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24 1728193
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25 2796256
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26 4524417
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27 7320639
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\end{filecontents}
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\begin{filecontents}{re-ssize.data}
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\end{filecontents}
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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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\\[-1mm]
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\LARGE Fast Regular Expression \\[-1mm]
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\LARGE Matching Using Derivatives\\[-3mm]
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\end{tabular}}
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\begin{center}
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%\includegraphics[scale=0.3]{pics/ante1.jpg}\hspace{5mm}
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%\includegraphics[scale=0.31]{pics/ante2.jpg}\\
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%\footnotesize\textcolor{gray}{Antikythera automaton, 100 BC (Archimedes?)}
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\end{center}
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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: & N\liningnums{7.07} (North Wing, Bush House)\\
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%Slides: & KEATS
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Student: & Chengsong Tan\\
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Supervisor: & Christian Urban \\
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Date: & 2019/5/10
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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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\begin{frame}[t]
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16
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\frametitle{Regular Expressions}
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Their inductive definition:\\
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\hspace{10pt}
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\vspace{100pt}
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\begin{textblock}{6}(1.5,3.5)
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\begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
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\bl{$r$} & \bl{$::=$} & \bl{$\ZERO$} & nothing\\
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& \bl{$\mid$} & \bl{$\ONE$} & empty string / \pcode{""} / $[]$\\
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& \bl{$\mid$} & \bl{$c$} & character\\
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& \bl{$\mid$} & \bl{$r_1 + r_2$} & alternative / choice\\
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& \bl{$\mid$} & \bl{$r_1 \cdot r_2$} & sequence\\
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& \bl{$\mid$} & \bl{$r^*$} & star (zero or more)\\
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\end{tabular}
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\end{textblock}
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\begin{itemize}
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\item { Formalized by Stephen Coles Kleene in 1950s}
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\item {\bf What could be possibly interesting?}
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\iffalse
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\begin{frame}[t]
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\frametitle{Regular Expressions}
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15
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John Regehr {\small(Univ.~Utah, LLVM compiler hacker)}\smallskip\\
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\begin{bubble}[10.5cm]
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\bf ``\ldots{}It’s effectively a perpetual
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employment act for solid compiler hackers.''
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\end{bubble}
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\onslide<1->{
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\only<2>{
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\begin{itemize}
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\item {\bf Hardware is getting weirder
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rather than getting clocked faster}
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\begin{itemize}
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\item Almost all processors are
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multicores nowadays and it looks like there is increasing asymmetry in
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resources across cores. Processors come with vector units, crypto
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accelerators etc. We have DSPs, GPUs,
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ARM big.little, and Xeon Phi. This is only scratching the
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surface.
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\end{itemize}
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\end{itemize}}
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\only<3>{
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\begin{itemize}
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\item {\bf We’re getting tired of low-level languages and
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their associated security disasters}
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\begin{itemize}
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\item
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We want to write new code, to
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whatever extent possible, in safer, higher-level
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languages. Compilers are caught right in the middle of these
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opposing trends: one of their main jobs is to help bridge the large
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and growing gap between increasingly high-level languages and
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increasingly wacky platforms.
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\end{itemize}
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\end{itemize}}}
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\end{frame}
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\fi
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\iffalse
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\begin{frame}[c]
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\frametitle{Why Bother?}
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\begin{columns}[t]
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\begin{column}{.5\textwidth}
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Ruby, Python, Java 8\medskip\\
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\begin{tikzpicture}\footnotesize
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\begin{axis}[
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xlabel={$n$},
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x label style={at={(1.05,0.0)}},
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ylabel={time in secs},
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enlargelimits=false,
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xtick={0,5,...,30},
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xmax=33,
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ymax=35,
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ytick={0,5,...,30},
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scaled ticks=false,
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axis lines=left,
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width=5.5cm,
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height=4cm,
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legend entries={Python,Ruby},
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legend pos=north west,
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legend cell align=left]
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\addplot[blue,mark=*, mark options={fill=white}] table {re-python.data};
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\addplot[brown,mark=triangle*, mark options={fill=white}] table {re-ruby.data};
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}\footnotesize
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\begin{axis}[
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xlabel={$n$},
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x label style={at={(1.05,0.0)}},
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ylabel={time in secs},
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enlargelimits=false,
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xtick={0,5,...,30},
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xmax=33,
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ymax=35,
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ytick={0,5,...,30},
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scaled ticks=false,
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axis lines=left,
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width=5.5cm,
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height=4cm,
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legend entries={Python, Java 8},
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legend pos=north west,
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legend cell align=left]
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\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
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\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
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\end{axis}
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\end{tikzpicture}
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\end{column}
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\begin{column}{.5\textwidth}
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Us (after next lecture)\medskip\\
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\begin{tikzpicture}\footnotesize
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\begin{axis}[
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xlabel={$n$},
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x label style={at={(1.07,0.0)}},
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ylabel={time in secs},
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enlargelimits=false,
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xtick={0,5000,...,10000},
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xmax=11000,
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ymax=35,
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ytick={0,5,...,30},
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scaled ticks=false,
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axis lines=left,
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width=5.5cm,
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height=4cm]
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\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
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\addplot[black,mark=square*,mark options={fill=white}] table {re3.data};
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\end{axis}
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\end{tikzpicture}
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\begin{tikzpicture}\footnotesize
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\begin{axis}[
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xlabel={$n$},
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x label style={at={(1.07,0.0)}},
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ylabel={time in secs},
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enlargelimits=false,
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ymax=35,
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ytick={0,5,...,30},
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scaled ticks=false,
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axis lines=left,
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width=5.5cm,
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height=4cm]
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\addplot[black,mark=square*,mark options={fill=white}] table {re3a.data};
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\end{axis}
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\end{tikzpicture}
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\end{column}
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\end{columns}\bigskip
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\small\centering
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matching \texttt{[a?]\{n\}[a]\{n\}} and \texttt{(a*)*b}
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against $\underbrace{\texttt{a}...\texttt{a}}_n$
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\end{frame}
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\fi
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}[c]
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368 |
\frametitle{Catastrophic Backtracking}
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369 |
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\begin{columns}
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\begin{column}{.5\textwidth}
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\begin{tikzpicture}
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\begin{axis}[
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xlabel={$n$},
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x label style={at={(1.07,0.0)}},
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ylabel={time in secs},
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16
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%y label style={at={(0.06,0.5)}},
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15
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enlargelimits=false,
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xtick={0,5,...,30},
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xmax=33,
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ymax=45,
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ytick={0,10,...,40},
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|
384 |
scaled ticks=false,
|
|
|
385 |
axis lines=left,
|
|
16
|
386 |
width=5cm,
|
|
|
387 |
height=4cm,
|
|
15
|
388 |
legend entries={Python, Java 8},
|
|
|
389 |
legend pos=north west]
|
|
|
390 |
\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
|
|
|
391 |
\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
|
|
|
392 |
\end{axis}
|
|
|
393 |
\end{tikzpicture}
|
|
16
|
394 |
|
|
15
|
395 |
\begin{tikzpicture}
|
|
|
396 |
\begin{axis}[
|
|
|
397 |
xlabel={$n$},
|
|
16
|
398 |
x label style={at={(1.07,0.0)}},
|
|
15
|
399 |
ylabel={time in secs},
|
|
16
|
400 |
%y label style={at={(0.06,0.5)}},
|
|
15
|
401 |
%enlargelimits=false,
|
|
|
402 |
%xtick={0,5000,...,30000},
|
|
|
403 |
xmax=65000,
|
|
|
404 |
ymax=45,
|
|
|
405 |
ytick={0,10,...,40},
|
|
|
406 |
scaled ticks=false,
|
|
|
407 |
axis lines=left,
|
|
16
|
408 |
width=5cm,
|
|
|
409 |
height=4cm,
|
|
15
|
410 |
legend entries={Java 9},
|
|
|
411 |
legend pos=north west]
|
|
|
412 |
\addplot[cyan,mark=*, mark options={fill=white}] table {re-java9.data};
|
|
|
413 |
\end{axis}
|
|
|
414 |
\end{tikzpicture}
|
|
|
415 |
\end{column}
|
|
16
|
416 |
\end{columns}\bigskip
|
|
|
417 |
\center
|
|
|
418 |
matching \texttt{(a*)*b}
|
|
|
419 |
against $\underbrace{\texttt{a}...\texttt{a}}_n$
|
|
15
|
420 |
\end{frame}
|
|
|
421 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
422 |
|
|
|
423 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
16
|
424 |
\begin{frame}[fragile]
|
|
|
425 |
\frametitle{Impact}
|
|
|
426 |
|
|
|
427 |
\begin{itemize}
|
|
|
428 |
\item Network Traffic Analysis
|
|
|
429 |
\begin{itemize}
|
|
|
430 |
\item Snort: > 5 million downloads
|
|
|
431 |
\item Bro: > 10000 downloads
|
|
|
432 |
\item thousands of regexes
|
|
|
433 |
\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\medskip
|
|
|
434 |
|
|
|
435 |
\end{itemize}
|
|
|
436 |
|
|
|
437 |
\begin{verbatim}
|
|
|
438 |
Jan 2 00:53:19 talisker sshd: Received disconnect from 110.53.183.227: [preauth]
|
|
|
439 |
Jan 2 00:58:31 talisker sshd: Received disconnect from 110.53.183.252: [preauth]
|
|
|
440 |
Jan 2 01:01:28 talisker sshd: Received disconnect from 221.194.47.236: [preauth]
|
|
|
441 |
Jan 2 01:03:59 talisker sshd: Received disconnect from 110.53.183.228: [preauth]
|
|
|
442 |
Jan 2 01:06:53 talisker sshd: Received disconnect from 221.194.47.245: [preauth]
|
|
|
443 |
...
|
|
|
444 |
\end{verbatim}
|
|
|
445 |
|
|
|
446 |
|
|
|
447 |
\item Compilers: lexical analysis
|
|
|
448 |
\end{itemize}
|
|
|
449 |
|
|
|
450 |
\end{frame}
|
|
|
451 |
|
|
|
452 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
453 |
|
|
|
454 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
15
|
455 |
\begin{frame}[c]
|
|
|
456 |
\frametitle{Evil Regular Expressions}
|
|
|
457 |
|
|
|
458 |
\begin{itemize}
|
|
16
|
459 |
%\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\medskip
|
|
15
|
460 |
\item Evil regular expressions\medskip
|
|
|
461 |
\begin{itemize}
|
|
|
462 |
\item \bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}
|
|
|
463 |
\item \bl{$(a^*)^*\cdot b$}
|
|
|
464 |
\item \bl{$([a$\,-\,$z]^+)^*$}
|
|
|
465 |
\item \bl{$(a + a \cdot a)^*$}
|
|
|
466 |
\item \bl{$(a + a^?)^*$}
|
|
16
|
467 |
\item \bl{$\^(.*?,)\{11\}P$}
|
|
|
468 |
\item \bl{$<html>.*?<head>.*?<title>.*?</title>.*?</head>.*?<body[^>]*>.*?</body>.*?</html>$}
|
|
|
469 |
\end{itemize}
|
|
|
470 |
|
|
|
471 |
\item Pearl Compatible Regular Expression(PCRE) \bl{$(r) \backslash 1$}
|
|
15
|
472 |
\end{itemize}
|
|
|
473 |
|
|
16
|
474 |
\end{frame}
|
|
|
475 |
|
|
|
476 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
477 |
|
|
|
478 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
479 |
|
|
|
480 |
\begin{frame}[c]
|
|
|
481 |
\frametitle{A Concrete Example}
|
|
|
482 |
\begin{adjustwidth*}{}{-1.2cm}
|
|
|
483 |
\resizebox{13cm}{4cm}{
|
|
|
484 |
|
|
|
485 |
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
|
|
|
486 |
\node[state,initial] (q_0) {$0$};
|
|
|
487 |
\node[state] (q_1) [right = of q_0] {$1$};
|
|
|
488 |
\node[state] (q_2) [right=of q_1] {$2$};
|
|
|
489 |
\node (q_dots1) [right = of q_2] {$\cdots$};
|
|
|
490 |
\node [state] (q_n) [right = of q_dots1] {$n$};
|
|
|
491 |
\node [state] (q_n1) [right = of q_n] {$n+1$};
|
|
|
492 |
\node[state] (q_n2) [right=of q_n1] {$n+2$};
|
|
|
493 |
\node[state,accepting] (q_n3) [right=of q_n2] {$n+3$};
|
|
|
494 |
|
|
|
495 |
\path[->]
|
|
|
496 |
(q_0) edge [loop above] node {$*$} (q_0)
|
|
|
497 |
(q_0) edge node {$a$} (q_1)
|
|
|
498 |
(q_1) edge node {$*$} (q_2)
|
|
|
499 |
(q_2) edge node {$*$} (q_dots1)
|
|
|
500 |
(q_dots1) edge node{$*$} (q_n)
|
|
|
501 |
(q_n) edge node{$*$} (q_n1)
|
|
|
502 |
(q_n1) edge node{$*$} (q_n2)
|
|
|
503 |
(q_n2) edge node{$*$} (q_n3);
|
|
|
504 |
|
|
|
505 |
\draw [decorate,decoration={brace,amplitude=10pt,mirror,raise=10pt},yshift=0pt]
|
|
|
506 |
(q_2.south west) -- (q_n1.south east) node [black,midway,yshift = -2cm] {\footnotesize n states};
|
|
|
507 |
%\draw [decorate,decoration={brace,amplitude=10pt,mirror,raise=4pt},yshift=0pt]
|
|
|
508 |
%(3.5,0.65) -- (3.5,6.5) node [black,midway,xshift=0.8cm] {\footnotesize
|
|
|
509 |
%$P_2$};
|
|
|
510 |
\end{tikzpicture}
|
|
|
511 |
}
|
|
|
512 |
\end{adjustwidth*}
|
|
|
513 |
|
|
|
514 |
\begin{itemize}
|
|
|
515 |
\item
|
|
|
516 |
NFA accepting Regex $.*a.{n}bc$
|
|
|
517 |
\item
|
|
|
518 |
Matching the string aaaaaaaaaaaaaaa.....abc
|
|
|
519 |
\end{itemize}
|
|
|
520 |
\end{frame}
|
|
|
521 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
522 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
523 |
\begin{frame}[c]
|
|
|
524 |
\frametitle{Brzozowski Derivative}
|
|
|
525 |
|
|
|
526 |
\begin{itemize}
|
|
|
527 |
\item Brzozowski invented in his 1964 Phd thesis
|
|
|
528 |
\item Intuition: Chopping off the first character
|
|
|
529 |
|
|
|
530 |
\begin{center}
|
|
|
531 |
\bl{$A \backslash c \dn \{ s \;|\; c\!::\!s \in A\}$ }
|
|
|
532 |
\end{center}
|
|
|
533 |
\item
|
|
|
534 |
For \bl{$A = \{\textit{foo}, \textit{bar}, \textit{frak}\}$} then
|
|
|
535 |
|
|
|
536 |
\begin{center}
|
|
|
537 |
\bl{\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l}
|
|
|
538 |
$A \backslash f $ & $=$ & $\{\textit{oo}, \textit{rak}\}$\\
|
|
|
539 |
$A \backslash b $ & $=$ & $\{\textit{ar}\}$\\
|
|
|
540 |
$A \backslash a $ & $=$ & $\{\}$\pause
|
|
|
541 |
\end{tabular}}
|
|
|
542 |
\end{center}
|
|
|
543 |
\item
|
|
|
544 |
\begin{tabular}{rp{4cm}}
|
|
|
545 |
\bl {$r \,matches \,s=c_1c_2...c_n$}
|
|
|
546 |
\bl{$\Leftrightarrow$} \bl{$c_1c_2...c_n \in L(r)$} \bl{$\Leftrightarrow$}\\
|
|
|
547 |
\bl{$c_2...c_n \in L(r) \backslash c_1$}\\
|
|
|
548 |
\bl{$\Leftrightarrow$} \bl{$\cdots$}\\
|
|
|
549 |
\bl{$\Leftrightarrow$} \bl{$[] \in ((L(r)\backslash c_1) \backslash c_2)\cdots\backslash c_n$}
|
|
|
550 |
\end{tabular}
|
|
|
551 |
|
|
15
|
552 |
\end{itemize}
|
|
|
553 |
|
|
|
554 |
\end{frame}
|
|
|
555 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
16
|
556 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
557 |
|
|
|
558 |
\begin{frame}[c]
|
|
|
559 |
\frametitle{Previous Example}
|
|
|
560 |
|
|
|
561 |
\begin{center}
|
|
|
562 |
\begin{tikzpicture}
|
|
|
563 |
\begin{axis}[
|
|
|
564 |
xlabel={$n$},
|
|
|
565 |
x label style={at={(1.09,-0.15)}},
|
|
|
566 |
ylabel={time in secs},
|
|
|
567 |
scaled x ticks=false,
|
|
|
568 |
enlargelimits=false,
|
|
|
569 |
xtick distance=10000,
|
|
|
570 |
xmax=44000,
|
|
|
571 |
ytick={0,10,...,30},
|
|
|
572 |
ymax=35,
|
|
|
573 |
axis lines=left,
|
|
|
574 |
width=7cm,
|
|
|
575 |
height=3.5cm,
|
|
|
576 |
legend entries={Java \liningnums{9}+},
|
|
|
577 |
legend pos=north west,
|
|
|
578 |
legend cell align=left]
|
|
|
579 |
\addplot[blue,mark=square*,mark options={fill=white}] table {re-java9.data};
|
|
|
580 |
\end{axis}
|
|
|
581 |
\end{tikzpicture}
|
|
|
582 |
\end{center}
|
|
|
583 |
|
|
|
584 |
\begin{center}
|
|
|
585 |
\begin{tikzpicture}
|
|
|
586 |
\begin{axis}[
|
|
|
587 |
xlabel={$n$},
|
|
|
588 |
x label style={at={(1.09,0.0)}},
|
|
|
589 |
ylabel={time in secs},
|
|
|
590 |
scaled x ticks=false,
|
|
|
591 |
xtick distance=2000000,
|
|
|
592 |
enlargelimits=false,
|
|
|
593 |
xmax=6400000,
|
|
|
594 |
ytick={0,10,...,30},
|
|
|
595 |
ymax=35,
|
|
|
596 |
axis lines=left,
|
|
|
597 |
width=7cm,
|
|
|
598 |
height=3.5cm,
|
|
|
599 |
legend entries={Simple Scala},
|
|
|
600 |
legend pos=north west,
|
|
|
601 |
legend cell align=left]
|
|
|
602 |
%\addplot[green,mark=square*,mark options={fill=white}] table {re2a.data};
|
|
|
603 |
\addplot[black,mark=square*,mark options={fill=white}] table {re3a.data};
|
|
|
604 |
\end{axis}
|
|
|
605 |
\end{tikzpicture}
|
|
|
606 |
\end{center}
|
|
|
607 |
|
|
|
608 |
Regex: \bl{$(a^*)^* \cdot b$} \space\space\space\space\space\space
|
|
|
609 |
Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
|
|
|
610 |
|
|
|
611 |
\end{frame}
|
|
|
612 |
|
|
15
|
613 |
|
|
|
614 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
16
|
615 |
\begin{frame}[t]
|
|
|
616 |
\frametitle{Optimization}
|
|
15
|
617 |
|
|
|
618 |
\begin{center}
|
|
16
|
619 |
\begin{tikzpicture}
|
|
|
620 |
\begin{semilogyaxis}[
|
|
|
621 |
xlabel={$n$},
|
|
|
622 |
x label style={at={(1.05,0.0)}},
|
|
|
623 |
ylabel={regex size},
|
|
|
624 |
enlargelimits=false,
|
|
|
625 |
xtick={1,4,...,30},
|
|
|
626 |
xmax=33,
|
|
|
627 |
%ytick={0, 10,...,100},
|
|
|
628 |
scaled ticks=false,
|
|
|
629 |
axis lines=left,
|
|
|
630 |
width=9cm,
|
|
|
631 |
height=4.5cm,
|
|
|
632 |
legend entries={Simple Scala},
|
|
|
633 |
legend pos= south east,
|
|
|
634 |
legend cell align=left
|
|
|
635 |
]
|
|
|
636 |
\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
|
|
|
637 |
%\addplot[brown,mark=pentagon*, mark options={fill=white}] table {re-ssize.data};
|
|
|
638 |
%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};
|
|
|
639 |
%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
|
|
|
640 |
\end{semilogyaxis}
|
|
|
641 |
\end{tikzpicture}
|
|
|
642 |
\end{center}
|
|
|
643 |
Regex: \bl{$(a+aa)^* \cdot b$} \space\space\space\space\space\space
|
|
|
644 |
Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}\\
|
|
|
645 |
\begin{itemize}
|
|
|
646 |
\item
|
|
|
647 |
Solution: Simplification%(Sulzmann \& Lu)
|
|
|
648 |
\begin{itemize}
|
|
|
649 |
\item $r+(r+s) = r+r+s = r+s$
|
|
|
650 |
\item $1 \cdot r= r$
|
|
|
651 |
\end{itemize}
|
|
|
652 |
\end{itemize}
|
|
|
653 |
\end{frame}
|
|
|
654 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
655 |
\begin{frame}[t]
|
|
|
656 |
\frametitle{Optimization}
|
|
15
|
657 |
|
|
16
|
658 |
Regex: \bl{$(a+aa)^* \cdot b$} \space\space\space\space\space\space
|
|
|
659 |
Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
|
|
15
|
660 |
|
|
16
|
661 |
\begin{center}
|
|
|
662 |
\begin{tikzpicture}
|
|
|
663 |
\begin{axis}[
|
|
|
664 |
xlabel={$n$},
|
|
|
665 |
x label style={at={(1.05,0.0)}},
|
|
|
666 |
ylabel={regex size},
|
|
|
667 |
enlargelimits=false,
|
|
|
668 |
xtick={1,4,...,30},
|
|
|
669 |
xmax=33,
|
|
|
670 |
%ytick={0, 10,...,100},
|
|
|
671 |
scaled ticks=false,
|
|
|
672 |
axis lines=left,
|
|
|
673 |
width=9cm,
|
|
|
674 |
height=4.5cm,
|
|
|
675 |
legend entries={Simplification Applied},
|
|
|
676 |
legend pos= south east,
|
|
|
677 |
legend cell align=left
|
|
|
678 |
]
|
|
|
679 |
%\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
|
|
|
680 |
\addplot[black,mark=triangle*, mark options={fill=white}] table {re-ssize.data};
|
|
|
681 |
%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};
|
|
|
682 |
%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
|
|
15
|
683 |
\end{axis}
|
|
16
|
684 |
\end{tikzpicture}
|
|
|
685 |
\end{center}
|
|
15
|
686 |
\begin{itemize}
|
|
16
|
687 |
\item
|
|
|
688 |
Lexer? Not just matcher
|
|
|
689 |
\begin{itemize}
|
|
|
690 |
\item
|
|
|
691 |
Bit-Coded Regular Expression Parsing (Lasse Nielsen, Fritz Henglein 2011)
|
|
|
692 |
\item
|
|
|
693 |
Bit-Coded Regular Expression Parsing with Simplification (Sulzmann and Lu 2014)
|
|
15
|
694 |
\end{itemize}
|
|
|
695 |
|
|
16
|
696 |
\end{itemize}
|
|
|
697 |
\end{frame}
|
|
15
|
698 |
|
|
|
699 |
|
|
|
700 |
|
|
|
701 |
|
|
|
702 |
|
|
|
703 |
|
|
|
704 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
705 |
|
|
|
706 |
\begin{frame}[t]
|
|
16
|
707 |
\frametitle{Ongoing Work}
|
|
15
|
708 |
|
|
|
709 |
|
|
16
|
710 |
\begin{tikzpicture}
|
|
|
711 |
\begin{semilogyaxis}[
|
|
|
712 |
xlabel={$n$},
|
|
|
713 |
x label style={at={(1.05,0.0)}},
|
|
|
714 |
ylabel={regex size},
|
|
|
715 |
enlargelimits=false,
|
|
|
716 |
xtick={1,4,...,30},
|
|
|
717 |
xmax=33,
|
|
|
718 |
%ytick={0, 10,...,100},
|
|
|
719 |
scaled ticks=false,
|
|
|
720 |
axis lines=left,
|
|
|
721 |
width=9cm,
|
|
|
722 |
height=4.5cm,
|
|
|
723 |
legend entries={Naive, Simp},
|
|
|
724 |
legend pos= north west,
|
|
|
725 |
legend cell align=left
|
|
|
726 |
]
|
|
|
727 |
\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
|
|
|
728 |
\addplot[black,mark=triangle*, mark options={fill=white}] table {re-ssize.data};
|
|
|
729 |
%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};
|
|
|
730 |
%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
|
|
|
731 |
\end{semilogyaxis}
|
|
|
732 |
\end{tikzpicture}
|
|
15
|
733 |
|
|
|
734 |
\begin{itemize}
|
|
16
|
735 |
\item
|
|
|
736 |
Correctness of Sulzmann \& Lu's algorithm
|
|
15
|
737 |
|
|
16
|
738 |
\item
|
|
|
739 |
Size Bound $O(n^2t^2)$ of Dervatives (1995 Antimirov "Partial Derivative")
|
|
|
740 |
\item
|
|
|
741 |
More radical simplifications.
|
|
|
742 |
\item
|
|
|
743 |
Extend the algorithm to back-references.
|
|
|
744 |
\end{itemize}
|
|
15
|
745 |
\end{frame}
|
|
|
746 |
|
|
|
747 |
|
|
|
748 |
|
|
|
749 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
750 |
|
|
|
751 |
|
|
|
752 |
|
|
|
753 |
|
|
|
754 |
|
|
|
755 |
|
|
|
756 |
|
|
|
757 |
|
|
|
758 |
|
|
|
759 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
760 |
\begin{frame}[c]
|
|
|
761 |
\frametitle{\begin{tabular}{c}\\[3cm]\alert{Questions?}\end{tabular}}
|
|
|
762 |
|
|
|
763 |
\mbox{}
|
|
|
764 |
\end{frame}
|
|
|
765 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
766 |
\end{document}
|
|
|
767 |
|
|
|
768 |
%%% Local Variables:
|
|
|
769 |
%%% mode: latex
|
|
|
770 |
%%% TeX-master: t
|
|
|
771 |
%%% End:
|
|
|
772 |
|