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- W1900508977 abstract "We consider the regular balanced model of satisfiability formula generation in conjunctive normal form (CNF), where each literal participates in equal number of clauses and there are k literals participating in a clause. We say that a formula is p-satisfying if there is a truth assignment satisfying 1-2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-k</sup> +p2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>-k</sup> fraction of clauses. Using the first moment method we determine upper bound on the threshold clause density such that there are no p-satisfying assignments with high probability above this upper bound. There are two aspects in deriving the lower bound using the second moment method. The first aspect is, given any p ∈ (0;1) and k, evaluate the lower bound on the threshold. This evaluation is numerical in nature. The second aspect is to derive the lower bound as a function of p for large enough k. We address the first aspect and evaluate the lower bound on the p-satisfying threshold using the second moment method. Based on the numerical evaluation, we observe that as k increases the ratio of the lower bound and the upper bound seems to converge to one." @default.
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- W1900508977 date "2010-09-01" @default.
- W1900508977 modified "2023-10-03" @default.
- W1900508977 title "Bounds on thresholds related to maximum satisfiability of regular random formulas" @default.
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- W1900508977 doi "https://doi.org/10.1109/istc.2010.5613816" @default.
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