The number of k-SAT functions

Authors:
Béla Bollobás;Graham R. Brightwell
Affiliations:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee and Trinity College, Cambridge CB2 1TQ, United Kingdom;Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom
Venue:
Random Structures & Algorithms
Year:
2003

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Abstract

We study the number SAT(k; n) of Boolean functions of n variables that can be expressed by a k-SAT formula. Equivalently, we study the number of subsets of the n-cube 2n that can be represented as the union of (n - k)-subcubes. In The number of 2-SAT functions (Isr J Math, 133 (2003), 45-60) the authors and Imre Leader studied SAT(k; n) for k ≤ n/2, with emphasis on the case k= 2. Here, we prove bounds on SAT(k; n) for k ≥ n/2; we see a variety of different types of behavior.