  We consider the unbinding of a directed polymer in a random media from a wall
in $d=1+1$ dimensions and a simple one-dimensional model for DNA unzipping.
Using the replica trick we show that the restricted partition functions of
these problems are {\em identical} up to an overall normalization factor. Our
finding gives an example of a generalization of the stochastic matrix form
decomposition to disordered systems; a method which effectively allows to
reduce dimensionality of the problem. The equivalence between the two problems,
for example, allows us to derive the probability distribution for finding the
directed polymer a distance $z$ from the wall. We discuss implications of these
results for the related Kardar-Parisi-Zhang equation and the asymmetric
exclusion process.
