could you be a bit more precise with your definition of the language you'd
like to show is undecidable? try to phrase it as a decision question that
results in a language of strings over some finite alphabet, and then maybe
you can get somewhere, with a reduction, for instance.

i'm not sure how you intend to define undecidability in the face of
randomness, or even what your question is really asking.

a natural way to use computability to include the flavor of randomness is to
bound the number of bad cases. i.e., to imagine that something is happening
either uniformly at random or with a particular distribution, and to bound
the probability in the uniform case is just to bound the number of bad cases
in the deterministic case. but you have to be careful about how you state
this.

it could be a fairly straightforward undecidability result, but it depends
upon the question that you're asking.

PS i tried to email you directly instead, but apparently your return email
address is invalid...

s.
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