Variants of Solomonoff induction

This page lists some variants of Solomonoff induction.

For determinism, I think "deterministic" is the same as "Solomonoff prior" and "stochastic" is the same as "universal mixture".

For discrete vs continuous, I think this just means whether the prior we define is over finite strings or over infinite sequences (where we want to know the probability of an infinite sequence starting with a given finite string).

Source	Formula	Determinism	Type of machine used	Discrete vs continuous
LessWrong Wiki	$m(y_0)={\sum }_{p\in \mathcal{P}:U(p)=y_0}{2}^{-\ell (p)}$ where $\mathcal{P}$ is the set of self-delimiting programs	Deterministic	Page doesn't say, but uses self-delimiting programs and it's discrete, so prefix Turing machine?	Discrete because the output string $y_0$ is finite
Scholarpedia discrete universal a priori probability	$m(x)={\sum }_{p:U(p)=x}{2}^{-\ell (p)}$ where the sum is over halting programs	deterministic?	prefix Turing machine	discrete
Scholarpedia continuous universal a priori probability	$M(x)={\sum }_{p:U(p)=x*}{2}^{-\ell (p)}$ where the sum is over minimal programs	deterministic?	Monotone Turing machine	Continuous
Sterkenburg (p. 22)	$P_{\mathrm{I}}(\sigma )=\underset{n\to \mathrm{\infty }}{lim}\frac{\left|T_{\sigma ,n}\right|}{T_n}$ where $T_n$ is the set of all halting (valid) inputs of length $n$ to the reference machine $U$, $T_{\sigma ,n}$ is the set of all halting (valid) inputs of length $n$ that output something starting with $\sigma$