  For string theory on AdS$_3$ with pure NS-NS flux a complete set of DDF
operators is constructed, from which one can read off the symmetry algebra of
the spacetime CFT. Together with an analysis of the spacetime spectrum, this
allows us to show that the CFT dual of superstring theory on ${\rm AdS}_3
\times {\rm S}^3 \times \mathbb{T}^4$ for generic NS-NS flux is the symmetric
orbifold of $({\cal N}=4$ Liouville theory$)\times \mathbb{T}^4$. For the case
of minimal flux ($k=1$), the Liouville factor disappears, and we just obtain
the symmetric orbifold of $\mathbb{T}^4$, thereby giving further support to a
previous claim. We also show that a similar analysis can be done for bosonic
string theory on ${\rm AdS}_3 \times X$.
