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- W2011639573 abstract "It is known that random k-SAT instances with at least $cn$ clauses, where $c =nobreak c_k$ is a suitable constant, are unsatisfiable (with high probability). We consider the problem to certify efficiently the unsatisfiability of such formulas. A backtracking-based algorithm of Beame et al. [SIAM J. Comput.,} 31 (2002), pp. 1048--1075] shows that k-SAT instances with at least $n^{k-1}/(log n)^{k-2}$ clauses can be certified unsatisfiable in polynomial time. We employ spectral methods to improve on this bound. For even $kge 4$ we present a polynomial time algorithm which certifies random k-SAT instances with at least $n^{(k/2)+o(1)}$ clauses as unsatisfiable (with high probability). For odd k we focus on 3-SAT instances and obtain an efficient algorithm for formulas with at least $n^{3/2+varepsilon}$ clauses, where $varepsilon >0$ is an arbitrary constant." @default.
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- W2011639573 date "2005-01-01" @default.
- W2011639573 modified "2023-10-14" @default.
- W2011639573 title "Recognizing More Unsatisfiable Random <i>k</i>-SAT Instances Efficiently" @default.
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- W2011639573 doi "https://doi.org/10.1137/s009753970444096x" @default.
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