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I'm looking for hints on formal reasoning capturing notion of indistinguishability, that is, the same probability distribution of a random variable. Such a variable could be sampled from 0/1 space while considering XOR games with random bits, or it could be sampled from a large ring. The latter case would be equipped with modular addition.

At best, any known way to conclude that distribution of the sum with a random variable with flat distribution is flat? Alternatively, what kind of reasoning about probabilities is doable with Z3?

The best match that I came across is probably reasoning about Bayesian Belief Networks (Michael Huth etal at Esorics), still feeling lost. So, where to start from? Thank you.

Vadym Fedyukovych
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Can't really answer the question, but it may be of interest that we recently designed a (very specialized) model checker for (some) probabilistic systems based on Z3. There's a paper about it and an implementation. In our very special setting everything is discretized, so it may be possible to answer questions of 'flatness' or similar, but it would probably still be very expensive.

Christoph Wintersteiger
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