Almost every 2-SAT function is unate

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Almost every 2-SAT function is unate

Bollobás, Brightwell and Leader [2] showed that there are at most 2( n 2)+o(n 2) 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, finding the number of 2-SAT functions on n variables to be 2( n 2)+n(1 + o(1)). As a corollary of...

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Almost 2-SAT is Fixed-Parameter Tractable

We consider the following problem. Given a 2-CNF formula, is it possible to remove at most k clauses so that the resulting 2-CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer Science under the names ’Almost 2SAT’, ’All-but-k 2-SAT’, ’2-CNF deletion’, ’2-SAT deletion’. The status of fixed-parameter tractability of this problem is a long-s...

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We consider the following problem. Given a 2-cnf formula, is it possible to remove at most k clauses so that the resulting 2-cnf formula is satisfiable? This problem is known to different research communities in theoretical computer science under the names Almost 2-SAT, All-but-k 2-SAT, 2-cnf deletion, and 2-SAT deletion. The status of the fixed-parameter tractability of this problem is a long-...

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ژورنال

عنوان ژورنال: Israel Journal of Mathematics

سال: 2007

ISSN: 0021-2172,1565-8511

DOI: 10.1007/s11856-007-0081-z