  We illustrate the basic notions of {\em additional non-isospectral
symmetries} and their interplay with the discrete {\em \DB transformations} of
integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili}
(\cKP) integrable hierarchies. As a main application we present the solution of
discrete multi-matrix string models in terms of Wronskian $\t$-functions of
graded $SL(m,1)$ \cKP hierarchies.
