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The issue with trying to apply Kolmogorov complexity to extremely small data (4 digits here) is that the universal Turing machine itself might take more than 4
by sn41 8y ago
The issue with trying to apply Kolmogorov complexity to extremely small data (4 digits here) is that the universal Turing machine itself might take more than 4 digits to write down. In principle, one could extend it to any sufficiently long pair of n digits, and then the question would be mathematically robust (though still uncomputable).
Also, for what it's worth, for large enough n, probably there are no interesting short answers. C(x|y) - the conditional complexity of any string x given any other string y is close to maximum (approximately the length of x) for most pairs x and y. This means, for most pairs x and y, there will be no simple short equations connecting x to y, regardless of the mathematical operators we take.