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The structure of the set of satisfying assignments for a random k-CNF

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Abstract

Let F k (n, m) be a random k-CNF obtained by a random, equiprobable, and independent choice of m brackets from among all k-literal brackets on n variables. We investigate the structure of the set of satisfying assignments of F k (n, m). A method is proposed for finding r(k, s)such that the probability of presence of ns-dimensional faces (0 < s < 1) in the set of satisfying assignments of the formula F k s(n, r(k, s)n) goes to 1 as n goes to infinity. We prove the existence of a sequential threshold for the property of having ns-dimensional faces (0 < s < 1). In other words, there exists a sequence r n (k, s) such that the probability of having an ns-dimensional face in the set of satisfying assignments of the formula F k (n, r n (k, s)(1 + d)n) goes to 0 for all d > 0 and to 1 for all d < 0.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    F. Yu. Vorob’ev

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  1. F. Yu. Vorob’ev
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Correspondence to F. Yu. Vorob’ev.

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Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 61–95, 2007.

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Vorob’ev, F.Y. The structure of the set of satisfying assignments for a random k-CNF. Comput Math Model 19, 304–331 (2008). https://doi.org/10.1007/s10598-008-9006-x

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