- The problem of stochastic sequential machines (SSM) synthesis is addressed and its relationship with the constrained sequence generation problem which arises during power estimation is discussed. In power estimation, one has to generate input vector sequences that satisfy a given statistical behavior (in terms of transition probabilities and correlations among bits) and/or to make these sequences as short as possible so as to improve the efficiency of power simulators. SSMs can be used to solve both problems. Based on Moore-type machines, a general procedure for SSM synthesis is revealed and a new framework for sequence characterization is built to match designer's needs for sequence generation or compaction. As results demonstrate, compaction ratios of 1-2 orders of magnitude can be obtained without much loss in accuracy of total power estimates.