You defined "m" as the measuring function which is not the pseudo-random number generator itself. I guess I don't understand your definitions.
In any case it's pretty obvious you have have deterministic chaotic output from which you cannot practically (or even in theory) recover the internal workings of the system that generated them. Take just a regular pseudorandom number generator or a cellular automata.
> In any case it's pretty obvious you have have deterministic chaotic output from which you cannot practically (or even in theory)
Solomonoff induction says otherwise. Of course it might take a stupendously large number of samples, but as the number of samples goes to infinity, the probability of reproducing the PRNG goes to 1.
In any case it's pretty obvious you have have deterministic chaotic output from which you cannot practically (or even in theory) recover the internal workings of the system that generated them. Take just a regular pseudorandom number generator or a cellular automata.