Memoryless channel

We say that a channel is memoryless if \begin{align*} p(y_i \mid x_1, x_2, \dots, x_n, y_1, y_2, \cdots, y_{i-1})=p(y_i \mid x_i). \end{align*} In words, the output at the current time, only depends on the input at the current time, but nor on the output nor on the input at previous times.