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}.


A PDF file (287 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2006-01, together with your name and postal address to:
CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.
Phone: +44(0)-20-7955 7494.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk 


Introduction to the CDAM Research Report Series.
CDAM Homepage.


Copyright © London School of Economics & Political Science 2006