$re = '/(\$[^\n$]*[^\s$])(-|=|\+)([^\s$][^\n$]*\$)/';
$str = '\\end{theorem}
A $k$-periodic sequence has the property that $s_i = s_{i + k}$ for all $i = 0,1,\\dots$.
Thus a $k$-periodic sequence $(s_i)_{i = 0}^\\infty$ may be represented by any finite sequence $(s_i)_{i=a}^{a+k - 1}$, where $a$ is usually chosen to be $0$.
Sadly our Fibonacci sequence examples are not defined over a finite field but over the naturals and thus are not necessarily periodic.
Examples such as these may be interpreted to have a period of $\\infty$.
The period and related stability of linear recurrence sequences in regard to linear complexity has a very rich and broadly studied background~\\cite{DingZiaoShan1991}.
\\begin{theorem}
\\label{th: max period is m-sequence}
\\cite[Theorem~6.33]{LidlNiederreiter1994}
A linear recurrence sequence $s$ over a finite field $\\gf_2$ with linear complexity $n$ has a maximum possible period of $2^n-1$.
\\end{theorem}
\\begin{definition}
\\label{de: m-sequence}
A sequence which has maximum period for giv';
preg_match_all($re, $str, $matches, PREG_SET_ORDER, 0);
// Print the entire match result
var_dump($matches);
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php