Consider some finite string $x=(x_1,x_2,...,x_{n-1},x_n)$ that is drawn from a *non-stationary* process. Would it be possible to use the algorithmic probability formula, defined by Solomonoff as,
$$
P_M(x)=\sum_{i=1}^{\infty}2^{-|s_{i}(x)|}
$$
to predict $x_n$, by computing the probability $$P_M(x_n | x_1,...x_{n-1})=P_M(x_1,x_2,...,x_{n-1},x_n)/P_M(x_1,x_2,...,x_{n-1})$$? Or is it a necessity that the process that $x$ is drawn from be stationary?

Edit: Here $s_i(x)$ refers to the $i$-th program which generated $x=(x_1,x_2,...,x_{n-1})$ and we want to predict the probability that $x_n$ is either a $1$ or a $0$.