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319
Typical random 3SAT formulae and the satisfiability threshold
 in Proceedings of the Eleventh ACMSIAM Symposium on Discrete Algorithms
, 2000
"... Abstract: We present a new structural (or syntactic) approach for estimating the satisfiability threshold of random 3SAT formulae. We show its efficiency in obtaining a jump from the previous upper bounds, lowering them to 4.506. The method combines well with other techniques, and also applies to o ..."
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Cited by 97 (4 self)
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Abstract: We present a new structural (or syntactic) approach for estimating the satisfiability threshold of random 3SAT formulae. We show its efficiency in obtaining a jump from the previous upper bounds, lowering them to 4.506. The method combines well with other techniques, and also applies
Counting Models for 2SAT and 3SAT Formulae
"... We here present algorithms for counting models and maxweight models for 2sat and 3sat formulae. They use polynomial space and run in O(1.2561^n) and O(1.6737^n) time, respectively, where n is the number of variables. This is faster than the previously best algorithms for counting nonweighted model ..."
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Cited by 7 (0 self)
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We here present algorithms for counting models and maxweight models for 2sat and 3sat formulae. They use polynomial space and run in O(1.2561^n) and O(1.6737^n) time, respectively, where n is the number of variables. This is faster than the previously best algorithms for counting non
A backbonesearch heuristic for efficient solving of hard 3SAT formulae£
"... Of late, new insight into the study of random�SAT formulae has been gained from the introduction of a concept inspired by models of physics, the ‘backbone’ of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of clauses. In ..."
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improvement over the best current algorithms, making it possible to handle unsatisfiable hard 3SAT formulae up to 700 variables. 1
A backbonesearch heuristic for efficient solving of hard 3SAT formulae
, 2001
"... Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of ..."
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Cited by 77 (1 self)
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Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number
On the satisfiability threshold and clustering of solutions of random 3Sat formulas
, 2007
"... ..."
Bounding the unsatisfiability threshold of random 3SAT
"... We lower the upper bound for the threshold for random 3SAT from 4.6011 to 4.596 through two different approaches, both giving the same result. (Assuming the threshold exists, as is generally believed but still not rigorously shown.) In both approaches, we start with a sum over all truth assignments ..."
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Cited by 44 (3 self)
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assignments that appears in an upper bound by Kirousis et al. to the the probability that a random 3SAT formula is satisfiable. In the first approach, this sum is reformulated as the partition function of a spin system consisting of n sites each of which may assume the values 0 or 1. We then obtain
Recognizing more random unsatisfiable 3SAT instances efficiently
, 2003
"... We show that random 3SAT formulas with poly(log n) · n^(3/2+o(1)) clauses can be efficiently certified as unsatisfiable. This improves a previous bound of n^(3/2+&epsilon) clauses. There &epsilon > 0 is a constant. ..."
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Cited by 6 (1 self)
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We show that random 3SAT formulas with poly(log n) · n^(3/2+o(1)) clauses can be efficiently certified as unsatisfiable. This improves a previous bound of n^(3/2+&epsilon) clauses. There &epsilon > 0 is a constant.
Optimal myopic algorithms for random 3SAT
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Let F 3 (n; m) be a random 3SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 \Gamma n 3 \Delta possible 3clauses over n variables. It has been conjectured that there exists a constant r 3 such that for any ffl ? 0, F 3 (n; (r 3 \Gamma ffl)n ..."
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Cited by 72 (9 self)
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Let F 3 (n; m) be a random 3SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 \Gamma n 3 \Delta possible 3clauses over n variables. It has been conjectured that there exists a constant r 3 such that for any ffl ? 0, F 3 (n; (r 3 \Gamma ffl
On Random 3SAT
, 1999
"... . We prove that a random Boolean 3SAT formula on n variables with 4:596n clauses is almost certainly unsatisfiable, in the sense that the probability of it being satisfiable tends to 0 as n !1. 1. Introduction and results The random 3SAT problem is the following: Let x 1 ; : : : ; x n be n Boolea ..."
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. We prove that a random Boolean 3SAT formula on n variables with 4:596n clauses is almost certainly unsatisfiable, in the sense that the probability of it being satisfiable tends to 0 as n !1. 1. Introduction and results The random 3SAT problem is the following: Let x 1 ; : : : ; x n be n
Improved Bound for the PPSZ/SchöningAlgorithm for 3SAT
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 159
, 2005
"... Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable 3SAT formula can be found in expected running time at most O(1.3071 n). Its bound degenerates when the number of solutions increases. In 1999, Schöning proved an bound of O(1.3334 n) for 3SAT. In 2003, Iw ..."
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Cited by 16 (0 self)
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Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable 3SAT formula can be found in expected running time at most O(1.3071 n). Its bound degenerates when the number of solutions increases. In 1999, Schöning proved an bound of O(1.3334 n) for 3SAT. In 2003
Results 1  10
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319