Witness of unsatisfiability for a random 3-satisfiability formula
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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Physical Review E, Volume 87, issue 5, pp. 1-10
Abstract
The random 3-satisfiability (3-SAT) problem is in the unsatisfiable (UNSAT) phase when the clause density α exceeds a critical value αs≈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 clause density α>19. We then construct Feige-Kim-Ofek witnesses for single 3-SAT instances through a simple random sampling algorithm and a focused local search algorithm. The random sampling algorithm works only when α scales at least linearly with the variable number N, but the focused local search algorithm works for clause density α>cNb with b≈0.59 and prefactor c≈8. The exponent b can be further decreased by enlarging the single parameter S of the focused local search algorithm.Description
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Wu, L-L, Zhou, H-J, Alava, M, Aurell, E & Orponen, P 2013, 'Witness of unsatisfiability for a random 3-satisfiability formula', Physical Review E, vol. 87, no. 5, 052807, pp. 1-10. https://doi.org/10.1103/PhysRevE.87.052807