It is well known that the stochastic approach using the HMM and dynamic programming-based search is particularly suited to the analysis of time series signals including on-line handwriting. The starting point of this research is a network of HMMs which models the whole set of characters. Then it is followed by the assertion that the HMM for the on-line script can be applied to not only on-line character recognition but also to the handwriting synthesis and even pen-trajectory recovery in off-line character images. The solutions to these problems are based on the single network of HMMs and the single principle of DP-based state-observation alignment. Given an observation sequence, the search for the best path in the network corresponds to the recognition. Given a character model, the search for the best observation sequence corresponds to the handwriting generation. The proposed framework has been shown to work nicely through a set of tests on Korean characters.