  G. Fici proved that a finite word has a minimal suffix automaton if and only
if all its left special factors occur as prefixes. He called LSP all finite and
infinite words having this latter property. We characterize here infinite LSP
words in terms of $S$-adicity. More precisely we provide a finite set of
morphisms $S$ and an automaton ${\cal A}$ such that an infinite word is LSP if
and only if it is $S$-adic and all its directive words are recognizable by
${\cal A}$.
