Dynamic Time Warping (DTW) and Hidden Markov Model (HMM) are two well-studied non-linear sequence alignment ( or, pattern matching) algorithm. The research trend transited from DTW to HMM in approximately 1988-1990, since DTW is deterministic and lack of the power to model stochastic signals. In this report, I make a comprehensive literature study into this transition, and show that DTW and sto...