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On the Fraction of Satisfiable Clauses in Typical Formulas
 Extended Abstract in FOCS’03
, 2003
"... Given n Boolean variables x1,..., xn, a kclause is a disjunction of k literals, where a literal is a variable or its negation. A kCNF formula is a conjunction of a finite number of kclauses. Call such a formula psatisfiable if there exists a truth assignment satisfying a fraction 12k +p 2k of ..."
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Cited by 3 (1 self)
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Given n Boolean variables x1,..., xn, a kclause is a disjunction of k literals, where a literal is a variable or its negation. A kCNF formula is a conjunction of a finite number of kclauses. Call such a formula psatisfiable if there exists a truth assignment satisfying a fraction 12k +p 2k
Hard Satisfiable Clause Sets for Benchmarking Equivalence Reasoning Techniques
, 2005
"... A family of satisfiable benchmark instances in conjunctive normal form is introduced. The instances are constructed by transforming a random regular graph into a system of linear equations followed by clausification. Schemes for introducing nonlinearity to the instances are developed, making the ins ..."
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Cited by 2 (0 self)
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A family of satisfiable benchmark instances in conjunctive normal form is introduced. The instances are constructed by transforming a random regular graph into a system of linear equations followed by clausification. Schemes for introducing nonlinearity to the instances are developed, making
A New Lower Bound on the Maximum Number of Satisfied Clauses in MaxSAT and its Algorithmic Applications
"... In a formula F = (V, C) in conjunctive normal form (CNF), V is the set of variables and C is the multiset of clauses. We denote by sat(F) the maximum number of clauses of F that can be satisfied by a truth assignment. It is wellknown that for every CNF formula F = (V, C), sat(F) ≥ C/2 and the bo ..."
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Cited by 5 (4 self)
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In a formula F = (V, C) in conjunctive normal form (CNF), V is the set of variables and C is the multiset of clauses. We denote by sat(F) the maximum number of clauses of F that can be satisfied by a truth assignment. It is wellknown that for every CNF formula F = (V, C), sat(F) ≥ C/2
Satisfiability Conflict clause afterburner
"... In this report we investigate ways to improve the conflictdriven satisfiability solving architecture by postprocessing conflict clauses before learning them using lookahead as a (expensive) conflict clause minimization technique. We investigate the effects of reducing the conflict clause size as w ..."
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In this report we investigate ways to improve the conflictdriven satisfiability solving architecture by postprocessing conflict clauses before learning them using lookahead as a (expensive) conflict clause minimization technique. We investigate the effects of reducing the conflict clause size
Experimental Results on the Crossover Point in Satisfiability Problems
 In Proceedings of the Eleventh National Conference on Artificial Intelligence
, 1993
"... Determining whether a propositional theory is satisfiable is a prototypical example of an NPcomplete problem. Further, a large number of problems that occur in knowledge representation, learning, planning, and other areas of AI are essentially satisfiability problems. This paper reports on a series ..."
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Cited by 209 (3 self)
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of experiments to determine the location of the crossover point  the point at which half the randomly generated propositional theories with a given number of variables and given number of clauses are satisfiable  and to assess the relationship of the crossover point to the difficulty of determining
Analytic and algorithmic solution of random satisfiability problems
 Science
"... We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (Ksatisfiability). Expressions with a ratio of clauses to variables less than a threshold c are almost always satisfiable, whereas those with a ratio above this threshold are almost always ..."
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Cited by 196 (7 self)
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We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (Ksatisfiability). Expressions with a ratio of clauses to variables less than a threshold c are almost always satisfiable, whereas those with a ratio above this threshold are almost
On the Greedy Algorithm for Satisfiability
 INFORMATION PROCESSING LETTERS
, 1992
"... We show that for the vast majority of satisfiable 3CNF formulae, the local search heuristic that starts at a random truth assignment, and repeatedly flips the variable that improves the number of satisfied clauses the most, almost always succeeds in discovering a satisfying truth assignment. ..."
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Cited by 32 (0 self)
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We show that for the vast majority of satisfiable 3CNF formulae, the local search heuristic that starts at a random truth assignment, and repeatedly flips the variable that improves the number of satisfied clauses the most, almost always succeeds in discovering a satisfying truth assignment.
Critical Behavior in the Satisfiability of Random Boolean Formulae
 Science
, 1994
"... The satisfiability of randomly generated Boolean formulae with k variables per clause is a popular testbed for the performance of search algorithms in artificial intelligence and computer science. For k = 2, formulae are almost aways satisfiable when the ratio of clauses to variables is less than ..."
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Cited by 179 (11 self)
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The satisfiability of randomly generated Boolean formulae with k variables per clause is a popular testbed for the performance of search algorithms in artificial intelligence and computer science. For k = 2, formulae are almost aways satisfiable when the ratio of clauses to variables is less
On Modern ClauseLearning Satisfiability Solvers
, 2010
"... In this paper, we present a perspective on modern clauselearning SAT solvers that highlights the roles of, and the interactions between, decision making and clause learning in these solvers. We discuss two limitations of these solvers from this perspective and discuss techniques for dealing with t ..."
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Cited by 4 (0 self)
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In this paper, we present a perspective on modern clauselearning SAT solvers that highlights the roles of, and the interactions between, decision making and clause learning in these solvers. We discuss two limitations of these solvers from this perspective and discuss techniques for dealing
On the Satisfiability and Maximum Satisfiability of Random 3CNF Formulas
"... We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3CNF formula with n variables. We show that the pure literal rule by itself nds satisfying assignments for almost all 3CNF formulas with up to 1:63n clauses, but it fails for more than 1:7n clauses. As an ..."
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Cited by 92 (6 self)
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We analyze the pure literal rule heuristic for computing a satisfying assignment to a random 3CNF formula with n variables. We show that the pure literal rule by itself nds satisfying assignments for almost all 3CNF formulas with up to 1:63n clauses, but it fails for more than 1:7n clauses
Results 1  10
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1,071