For boolean functions, is there a name for the property that changing only a few input bits will change only a few output bits? (I want something analogous to continuity for the discrete world.)
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Hamming Lipschitz would work best, as one can use literally the same definition of a Lipschitz function on a metric space.
Oh yes, that's much better than trying to use the epsilon-delta criterion. +1 for "Hamming Lipschitz continous".