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Almost every 2-SAT function is unate

Allen, Peter ORCID: 0000-0001-6555-3501 (2007) Almost every 2-SAT function is unate. Israel Journal of Mathematics, 161 (1). pp. 311-346. ISSN 0021-2172

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Identification Number: 10.1007/s11856-007-0081-z


Bollob´as, Brightwell and Leader showed that there are at most 2^(n 2)+o(n2) 2-SAT functions on n variables, and conjectured that in fact the number of 2-SAT functions on n variables is 2^(n 2)+n(1 + o(1)). We prove their conjecture. As a corollary of this, we also find the expected number of satisfying assignments of a random 2-SAT function on n variables. We also find the next largest class of 2-SAT functions and show that if k = k(n) is any function with k(n) < n1/4 for all sufficiently large n, then the class of 2-SAT functions on n variables which cannot be made unate by removing 25k variables is smaller than 2(n 2)+n−kn for all sufficiently large n.

Item Type: Article
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Additional Information: © 2007 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 May 2012 15:10
Last Modified: 16 May 2024 00:39

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