I said the programs have a single output, instead of a probability distribution. It matches the sequence so far or it doesn’t, maybe programs are 100% eliminated or 100% not eliminated. The probabilistic nature comes entirely from the summing-over-all-programs part.
Yes, I’m using the same definition. The “deterministic programs” mentioned in my comment are programs that output a sequence of bits, not programs that output a probability distribution.
That definition is equivalent to a mixture of all possible computable distributions. I suppose that equivalence is an important and surprising fact about SI: how come it makes no difference whether you quantify over programs that output a sequence of bits, or programs that output a probability distribution? But yes, it is true.
Yes, I’m using the same definition. The “deterministic programs” mentioned in my comment are programs that output a sequence of bits, not programs that output a probability distribution.
That definition is equivalent to a mixture of all possible computable distributions. I suppose that equivalence is an important and surprising fact about SI: how come it makes no difference whether you quantify over programs that output a sequence of bits, or programs that output a probability distribution? But yes, it is true.