  We present an efficient algorithm for computing the LZ78 factorization of a
text, where the text is represented as a straight line program (SLP), which is
a context free grammar in the Chomsky normal form that generates a single
string. Given an SLP of size $n$ representing a text $S$ of length $N$, our
algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time
and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors.
We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the
time and space complexities becomes either $nL$, where $L$ is the length of the
longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity
which depends on the amount of redundancy that the SLP captures with respect to
substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where
$\sigma$ is the alphabet size, the latter is asymptotically at least as fast as
a linear time algorithm which runs on the uncompressed string when $\sigma$ is
constant, and can be more efficient when the text is compressible, i.e. when
$m$ and $n$ are small.
