\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\def \Bitstream{Bit Stream}
\def \bitstream{bit stream}
%opening
\title{Fast Regular Expression Matching using Parallel \Bitstream{}s}
\author{
{Robert D. Cameron} \\
\and
{Kenneth S. Herdy} \\
\and
{Ben Hull} \\
\and
{Thomas C. Shermer} \\
\\School of Computing Science
\\Simon Fraser University
}
\begin{document}
\date{}
\maketitle
\begin{abstract}
A data parallel regular expression matching method using the concept of bitstream technology
is introduced and studied in application to the problem of fast regular expression matching.
The method is based on the concept of parallel
\bitstream{} technology, in which parallel streams of bits are formed such
that each stream comprises bits in one-to-one correspondence with the
character code units of a source data stream.
On processors supporting W-bit addition operations, the method processes W source characters
in parallel and performs up to W finite state transitions per clock cycle.
Performance results show a dramatic speed-up over traditional and state-of-the-art alternatives.
\end{abstract}
\section{Introduction}
\label{Introduction}
%\input{introduction.tex}
Regular expresssion matching is an extensively studied problem with a multitude
of algorithms and software tools developed to the demands of particular problem contexts.
Given a text T$_{1..n}$ of n characters and a pattern P, the pattern matching problem can be
stated as follows. Find all the text positions of T that start an occurrence of P.
Alternatively, one may want all the final positions of occurrences. Some
applications require slightly different output such as the line that matches the pattern.
The pattern P can be just a simple string,
but it can also be, for example, a regular expression.
A regular expression, or pattern, is an expression that specifies a set of strings.
A regular expression is composed of (i) simple strings (ii) the empty or (ii)
union, concatenation and Kleene closure of other regular expressions.
To avoid parentheses it is assumed that the Kleene star has the highest priority,
next concatenation and then alternation, however, most formalisms provides grouping
operators to allow the definition of scope and operator precedence.
Readers unfamiliar with the concept of regular expression matching are referred
classical texts such as \cite{aho2007}.
Regular expression matching is commonly performed using a variety of
publically available software tools. The most prominent, UNIX grep,
Gnu grep, agrep, cgrep, nrgrep, and Perl regular
expressions \cite{Abou-assaleh04surveyof}.
Amongst these Gnu grep, agrep, and nrgrep are widely known and considered as
the fastest regular expression matching tools in practice \cite{}.
Of particular interest to this study are the performance oriented Gnu grep, agrep, and nrgrep.
% motivation / previous work
Although the finite state machine methods used in the scanning and parsing of
text streams is considered to be the hardest of the “13 dwarves” to parallelize
[1], parallel bitstream technology shows considerable promise for these types of
applications [3, 4]. In this approach, character streams are processed W positions
at a time using the W-bit SIMD registers commonly found on commodity processors
(e.g., 128-bit XMM registers on Intel/AMD chips). This is achieved by
first slicing the byte streams into eight separate basis bitstreams, one for each bit
position within the byte. These basis bitstreams are then combined with bitwise
logic and shifting operations to compute further parallel bit streams of interest.
We further increase the parallelism in our methods by introducing a new parallel
scanning primitive which we have coined 'Match Star' that returns all matches in a single
operation and eliminates the need for back tracking ... (ELABORATE)
--- STATE the content of the next sections. ---
We compare the performance of our parallel \bitstream{} techniques against
various grep concentrate on the simpler case of
reporting initial or final occurrence positions.
\section{Background}
\label{Background}
%\input{background.tex}
% Background
% History
Historically, the origins of regular expression matching date back to automata theory
and formal language theory developed by Kleene in the 1950s \cite{kleene1951representation}.
In 1959, Dana and Scott demonstrated that
NFAs can be simulated using Deterministic Finite Automata (DFA) in which each DFA
state corresponds to a set of NFA states.
Thompson, in 1968, is credited with the first construction to convert regular expressions
to nondeterministic finite automata (NFA) for regular expression matching.
Thompson’s publication \cite{thompson1968} marked the beginning of a long line of
regular expression implementations that construct automata for pattern matching.
The traditional technique [16] to search a regular expression of length m in
a text of length n is to first convert the expression into a non-deterministic
automaton (NFA) with O(m) nodes. It is possible to search the text using the
NFA directly in O(mn) worst case time. The cost comes from the fact that
more than one state of the NFA may be active at each step, and therefore all
may need to be updated. A more effcient choice is to convert the NFA into a
DFA. A DFA has only a single active state and allows to search the text at
O(n) worst-case optimal. The problem with this approach is that the DFA
may have O(2^m) states.
In general, the general process is first to build a
NFA from the regular expression and simulate the NFA on text input,
or alternatively to convert the NFA into a
DFA, optionally minimize the number of states in the DFA,
and finally simulate the DFA on text input.
\section{Methodology}
\label{Methodology}
%\input{methodology.tex}
\section{Experimental Results}
\label{results}
%\input{results.tex}
\section{Conclusion and Future Work}
\label{conclusion}
%\input{conclusion.tex}
{
\bibliographystyle{acm}
\bibliography{reference}
}
\end{document}