Space-Efficient Conversions from SLPs

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(n log(2) n) or in time O(gz log(2)(n/z)). We also show how to build a locally consistent grammar (LCG) of optimal size g(lc) = O(delta log n/delta) from the SLP within O(g + g(lc)) space and in O(n log g) time, where d is the substring complexity measure of T. Finally, we show how to build the LZ parse of T from such an LCG within O(g(lc)) space and in time O(z log(2) n log(2) (n/z)). All our results hold with high probability.