  We use the Kontsevich-Miwa transform to relate the different pictures
describing matter coupled to topological gravity in two dimensions: topological
theories, Virasoro constraints on integrable hierarchies, and a DDK-type
formalism. With the help of the Kontsevich-Miwa transform, we solve the
Virasoro constraints on the KP hierarchy in terms of minimal models dressed
with a (free) Liouville-like scalar. The dressing prescription originates in a
topological (twisted N=2) theory. The Virasoro constraints are thus related to
essentially the N=2 null state decoupling equations. The N=2 generators are
constructed out of matter, the `Liouville' scalar, and $c=-2$ ghosts. By a
`dual' construction involving the reparametrization $c=-26$ ghosts, the DDK
dressing prescription is reproduced from the N=2 symmetry. As a by-product we
thus observe that there are two ways to dress arbitrary $d\leq1$ or $d\geq25$
matter theory, that allow its embedding into a topological theory. By th e
Kontsevich-Miwa transform, which introduces an infinite set of `time' variables
$t_r$, the equations ensuring the vanishing of correlators that involve
BRST-exact primary states, factorize through the Virasoro generators expressed
in terms of the $t_r$. The background charge of these Virasoro generators is
determined by the topological central charge.
