A zero-one law for first-order logic on random images
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چکیده
For an n×n random image with independent pixels, black with probability p(n) and white with probability 1−p(n), the probability of satisfying any given firstorder sentence tends to 0 or 1, provided both p(n)n 2 k and (1 − p(n))n 2 k tend to 0 or +∞, for any integer k. The result is proved by computing the threshold function for basic local sentences, and applying Gaifman’s theorem.
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تاریخ انتشار 2016