## Approximating the unsatisfiability threshold of random formulas (1998)

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### BibTeX

@INPROCEEDINGS{Kirousis98approximatingthe,

author = {Lefteris M. Kirousis and Evangelos Kranakis and Danny Krizanc and Yannis C. Stamatiou},

title = {Approximating the unsatisfiability threshold of random formulas},

booktitle = {},

year = {1998},

pages = {253--269}

}

### Years of Citing Articles

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### Abstract

ABSTRACT: Let � be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number � such that if the ratio of the number of clauses over the number of variables of � strictly exceeds �, then � is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that ��5.191. This upper bound was improved by Kamath et al. to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of � is around 4.2. In this work, we define, in terms of the random formula �, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then � is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for � equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601�. In general, by letting the

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Citation Context ...erge to zero with n, we will get an equation in terms of r that gives the required bound for . To compute an upper bound for the second factor of the sum, we will make use of the Janson 's inequality =-=[7]-=-, which gives an estimate for the probability of the intersection of dependent events. We give the details in the first subsection of the present section. The computations that will then give a closed... |

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