The number of K-SAT Functions


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. © 2003 Wiley Periodicals, Inc.

Publication Title

Random Structures and Algorithms