Space-efficient conversions from SLPs

Given a straight-line program with $g$ rules for a text $T [1..n]$, with high probability we can build in the LZ77 parse of $T$ in $n\,\mathrm{polylog} (n)$ time and $O (g)$ space. We can also build a locally consistent grammar of optimal size $g' = O(\delta\log\frac{n}{\delta})$ in $O(n\log n)$ time and $O(g+g')$ space.