\documentclass[12pt]{article}
\usepackage{a4wide,alltt,xspace,times}
\newcommand{\Maxsub}[2]{\emph{maxsub}(#1,#2)}
\newcommand{\Substring}[3]{#1[#2..#3]}
\newcommand{\Matchpos}[2]{\emph{matchpos}(#1,#2)}
\newcommand{\Nats}{\textrm{I}\!\textrm{N}}
\newcommand{\Size}[1]{|#1|}

\begin{document}
Consider two strings \(p\) and \(t\) of length \(m\) and \(n\), respectively.
Let \(w\) be a string. 
\(\Maxsub{w}{p}\) is the longest prefix \(y\) of \(w\) such that 
\(y\) is a substring of \(p\). 
\(\Matchpos{y}{p}\) is the set of positions \(i\in[0,m-\Size{y}]\) such that
\(\Substring{p}{i}{\Size{y}-1}=y\).

The \emph{matching statistics} of \(t\) w.r.t.\ \(p\) is the function
\(mstats:[0,n-1]\to \Nats\times\Nats\)
defined by \(mstats(j)=(\Size{y},q)\) where 
\(y=\Maxsub{\Substring{t}{j}{n}}{p}\) and 
\(q\in\Matchpos{\Substring{t}{j}{n}}{p}\).
For a given threshold value \(\ell\geq 1\), the \(\ell\)-matching statistics
is the partial function
\(mstats_{\ell}:[0,n-1]\to \Nats\times\Nats\) defined by
\[
mstats_{\ell}(j)=\left\{
\begin{array}{ll}
mstats(j)&\mbox{if }mstats(j)\geq\ell\\
\bot&\mbox{otherwise}
\end{array}\right.
\]

We consider sequences \(T_{1},\ldots,T_{k}\) and a threshold value 
\(\ell\). The \emph{multi matching statistics problem} is to compute 
for each \(i,j\in[1,k]\), \(i\neq j\), the \(\ell\)-matching statistics
of \(T_{i}\) w.r.t.\ \(T_{j}\).
\end{document}
