On the hardness of approximate reasoning
Artificial Intelligence
Randomized algorithms: approximation, generation, and counting
Randomized algorithms: approximation, generation, and counting
ACSC '02 Proceedings of the twenty-fifth Australasian conference on Computer science - Volume 4
Counting Satisfying Assignments in 2-SAT and 3-SAT
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Improved upper bounds for 3-SAT
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An improved deterministic local search algorithm for 3-SAT
Theoretical Computer Science
A tighter bound for counting max-weight solutions to 2SAT instances
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
An improved Õ(1.234m)-time deterministic algorithm for SAT
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Computing #2SAT and #2UNSAT by binary patterns
MCPR'12 Proceedings of the 4th Mexican conference on Pattern Recognition
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The #SAT problem is a classical #P-complete problem even for monotone, Horn and two conjunctive formulas (the last known as #2SAT). We present a novel branch and bound algorithm to solve the #2SAT problem exactly. Our procedure establishes a new threshold where #2SAT can be computed in polynomial time. We show that for any 2-CF formula F with n variables where #2SAT(F) ≤ p(n), for some polynomial p, #2SAT(F) is computed in polynomial time. This is a new way to measure the degree of difficulty for solving #2SAT and, according to such measure our algorithm allows to determine a boundary between ‘hard’ and ‘easy’ instances of the #2SAT problem.