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Communication Dans Un Congrès Année : 2004

A zero-one law for first-order logic on random images

Résumé

For an $n\!\times\! n$ random image with independent pixels, black with probability $p(n)$ and white with probability $1\!-\!p(n)$, the probability of satisfying any given first-order sentence tends to $0$ or $1$, provided both $p(n)n^{\frac{2}{k}}$ and $(1-p(n))n^{\frac{2}{k}}$ tend to $0$ or $+\infty$, 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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Dates et versions

hal-00020672 , version 1 (14-03-2006)

Identifiants

Citer

David Coupier, Agnès Desolneux, Bernard Ycart. A zero-one law for first-order logic on random images. International Colloquium of Mathematics and Computer Science, Sep 2004, Vienne, Austria. pp.495-505, ⟨10.1007/978-3-0348-7915-6_48⟩. ⟨hal-00020672⟩
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