Lazyweb, do any interesting things happen if you define an analogue of Kolmogorov complexity in terms of an explicitly non-Turing-complete description language?
Unfortunately I don't think many "interesting things happen" aside from breaking the formal logicians' toys, since all the relevant computations are way outside the scope of practical computability anyway once you reach a certain size.
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But maybe there are some interesting results that can be had for moderately small sizes, e.g. on topics like password strength.
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