The number of 2-SAT functions

Authors

Béla Bollobás, University of MemphisFollow
Graham R. Brightwell, London School of Economics and Political ScienceFollow
Imre Leader, Trinity College CambridgeFollow

Abstract

Our aim in this paper is to address the following question: of the 22(n) Boolean functions on n variables, how many are expressible as 2-SAT formulae? In other words, we wish to count the number of different instances of 2-SAT, counting two instances as equivalent if they have the same set of satisfying assignments. Viewed geometrically, we are asking for the number of subsets of the n-dimensional discrete cube that are unions of (n - 2)-dimensional subcubes. There is a trivial upper bound of 24(n/2). the number of 2-SAT formulae. There is also an obvious lower bound of 2(n/2). corresponding to the monotone 2-SAT formulae. Our main result is that, rather surprisingly, this lower bound gives the correct speed: the number of 2-SAT functions is 2(1 + ο(1))n(2)/2.

Publication Title

Israel Journal of Mathematics

Recommended Citation

Bollobás, B., Brightwell, G., & Leader, I. (2003). The number of 2-SAT functions. Israel Journal of Mathematics, 133, 45-60. https://doi.org/10.1007/BF02773060