Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2001-11

December 2001

The number of k-SAT functions

Béla Bollobás and Graham R. Brightwell


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, LSE-CDAM-2000-08, the authors and Imre Leader studied SAT(k;n) for k $\le$ n/2, with emphasis on the case k=2. Here, we prove bounds on SAT(k;n) for k $\ge$ n/2; we see a variety of different types of behaviour.

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