Decoding, in models such as HMM that contains hidden variables, is the task that takes as input an HMM $\lambda = (A, B)$ and a sequence of observations $O = o_1 , ..., o_T$, and finds the most probable sequence of states $Q = q_1...q_T$. For part-of-speech tagging, the goal of HMM decoding is to choose the tag sequence $t_1...t_n$ that is most probable given the observation sequence of $n$ words $w_1...w_n$: $\hat t_{1:n} = \argmax_{t_1, ..., t_n} P(t_1...t_n|w_1...w_n)$