Figure 2

Reusing common expressions to speed up the forward algorithm. The actual computation of the likelihood of the observed sequence 10100010011001 given a specific HMM. The rectangles represent matrices and vectors and lines between them represent dependencies. In stage 1 the $C_{o_i}$ matrices are computed. The solid black lines show the amount of work performed, while the grey lines show the amount of work saved due to redundancy. C₂ is for example computed as the product C₁C₀, and this multiplication is saved three times. In the second stage α _T is computed from the compressed sequence and the $C_{o_i}$ matrices. As in Figure 1α _i is computed from α_i−1 and $C_{o_i}$.