It is shown that the Lyndon decomposition of a word of n symbols can b
e computed by an n-processor CRCW PRAM in 0(log n) time. Extensions of
the basic algorithm convey, within the same time and processors bound
s, efficient parallel solutions to problems such as finding the lexico
graphically minimum or maximum suffix for all prefixes of the input st
ring, and finding the lexicographically least rotation of all prefixes
of the input.