Abstract
It is known that random k-SAT instances with at least dn clauses where d = d k is a suitable constant are unsatisfiable (with high probability). This paper deals with the question to certify the unsatisfiability of a random 3-SAT instance in polynomial time. A backtracking based algorithm of Beame et al. works for random 3-SAT instances with at least n 2/ log n clauses. This is the best result known by now.
We improve the n 2/ log n bound attained by Beame et al. to n 3/2+ε for any ε > 0. Our approach extends the spectral approach introduced to the study of random k-SAT instances for k ≥ 4 in previous work of the second author.
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Friedman, J., Goerdt, A. (2001). Recognizing More Unsatisfiable Random 3-SAT Instances Efficiently. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_26
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DOI: https://doi.org/10.1007/3-540-48224-5_26
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