Abstract:The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density α exceeds a critical value α s ≈ 4.267. Rigorously proving the unsatisfiability of a given large 3-SAT instance is, however, extremely difficult. In this paper we apply the mean-field theory of statistical physics to the unsatisfiability problem, and show that a reduction to 3-XORSAT, which permits the construction of a specific type of UNSAT witnesses (Feige-Kim-Ofek witnesses), is possible when the claus… Show more
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