Abstract

We give algorithms that, given a straight-line program (SLP) with g rules that generates (only) a text T[1..n], build within O(g) space the Lempel-Ziv (LZ) parse of T (of z phrases) in time O(nlog2n) or in time O(gzlog2(n/z)). We also show how to build a locally consistent grammar (LCG) of optimal size glc=O(δlognδ) from the SLP within O(g+glc) space and in O(nlogg) time, where δ is the substring complexity measure of T. Finally, we show how to build the LZ parse of T from such an LCG within O(glc) space and in time O(zlog2nlog2(n/z)). All our results hold with high probability.