  We introduce a new class of straight-line programs (SLPs), named the Lyndon
SLP, inspired by the Lyndon trees (Barcelo, 1990). Based on this SLP, we
propose a self-index data structure of $O(g)$ words of space that can be built
from a string $T$ in $O(n \lg n)$ expected time, retrieving the starting
positions of all occurrences of a pattern $P$ of length $m$ in $O(m + \lg m \lg
n + occ \lg g)$ time, where $n$ is the length of $T$, $g$ is the size of the
Lyndon SLP for $T$, and $occ$ is the number of occurrences of $P$ in $T$.
