  We consider the canonical quantization scheme for $c \leq 1$ ($(p,q)$ -)
string theories and compare it with what is known from matrix model approach.
We derive explicitly a trivial ($\equiv $ topological) solution. We discuss a
``dressing" operator which in principle allows one to obtain a non-trivial
solution, but an explicit computation runs into a problem of analytic
continuation of the formal expressions for $\tau $-functions. We discuss also
the application of proposed scheme to the case of discrete matrix model and
consider some parallels with mirror symmetry and background independence in
string theory.
