Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2006-01

January 2006

Almost every 2-SAT function is unate

Peter Allen

Bollobs, Brightwell and Leader [2] found upper and lower bounds for the number of 2-SAT functions on n variables, and conjectured that in fact almost every 2-SAT function is unate: i.e., has a 2-SAT formula in which no variable's positive and negative literals both appear. We prove their conjecture.

As a corollary of this, we also find the average number of satisfying assignments of a 2-SAT function on n variables. We also find the next largest class of 2-SAT functions, and find an upper bound on the number of 2-SAT functions on n variables which cannot be made unate by removing 25k variables, for any k=k(n)<n^{1/4}.

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