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New upper bound for the #3SAT problem
"... We present a new deterministic algorithm for the #3SAT problem, based on the DPLL strategy. It uses a new approach for counting models of instances with low density. This allows us to assume the adding of more 2clauses than in previous algorithms. The algorithm achieves a running time of O(1.6423 ..."
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We present a new deterministic algorithm for the #3SAT problem, based on the DPLL strategy. It uses a new approach for counting models of instances with low density. This allows us to assume the adding of more 2clauses than in previous algorithms. The algorithm achieves a running time of O(1.6423 n) in the worst case which improves the current best bound of O(1.6737 n) by Dahllöf et al. 1
Faithful Representations and Moments of Satisfaction: Probabilistic Methods in Learning and Logic
, 1998
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On the Random Generation of 3SAT Instances
 LABORATOIRE BORDELAIS DE RECHERCHE EN INFORMATIQUE, UNIVERSITE BORDEAUX I
, 1995
"... Deep results have been obtained recently on randomly generated kSAT instances. They have ..."
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Deep results have been obtained recently on randomly generated kSAT instances. They have
New Polynomial Classes for #2SAT Established Via GraphTopological Structure
"... Abstract—We address the problem of designing efficient procedures for counting models of Boolean formulas and, in this task, we establish new classes of instances where #2SAT is solved in polynomial time. Those instances are recognized by the topological structure of the underlying graph of the inst ..."
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Abstract—We address the problem of designing efficient procedures for counting models of Boolean formulas and, in this task, we establish new classes of instances where #2SAT is solved in polynomial time. Those instances are recognized by the topological structure of the underlying graph of the instances. We show that, if the depthsearch over the constrained graph of a formula generates a tree where the set of fundamental cycles are disjointed (there are not common edges between any pair of fundamental cycles), then #2SAT is tractable. This class of instances do not set restrictions on the number of occurrences of a variable in a Boolean formula. Our proposal can be applied to impact directly in the reduction of the complexity time of the algorithms for other counting problems.
Determining the number of solutions to binary CSP instances
"... Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instances, where ..."
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Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2sat instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247 n · (d/2) n) time, or odd, in which case it runs in O(1.3247 n · ((d 2 + d + 2)/4) n/2) if d = 4 · k + 1, and O(1.3247 n · ((d 2 + d)/4) n/2) if d = 4 · k + 3. We also give an algorithm for counting the number of possible 3colourings of a given graph, which runs in O(1.8171 n), an improvement over our general algorithm gained by using problem specific knowledge.
The Good Old DavisPutnam . . .
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1999
"... As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the DavisPutnam procedure, we present an al ..."
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As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the DavisPutnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F . Let m and n be the number of clauses and variables of F , respectively, and let p denote the probability that a literal l of F occurs in a clause C of F , then the average running time of CDP is shown to be O(m n), where d = d e. The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
Chapter 35 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 finds satisfying assignments for almost all 3CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As a ..."
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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 finds satisfying assignments for almost all 3CNF formulas with up to 1.63n clauses, but it fails for more than 1.7n clauses. As an aside we show that the value of maximum satisfiability for random 3CNF formulas is tightly concentrated around its mean. 1
BOSE–EINSTEIN CONDENSATION IN THE K–SAT PROBLEM Diploma di Licenza
"... 1 k–SAT and Bose–Einstein condensation 2 ..."
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MINESWEEPER, #MINESWEEPER
, 2003
"... ”Hence the easiest way to ensure you always win: ..."
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Moments of satisfaction: statistical properties of a large random KCNF formula
, 1996
"... this paper we study the satassignment distribution and overlap, of a large random KCNF formula. In particular, we study analytically the second, third and fourth moments of the number of satisfying assignments and overlap between satisfying assignments. We show that for K ? 4 the average overlap b ..."
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this paper we study the satassignment distribution and overlap, of a large random KCNF formula. In particular, we study analytically the second, third and fourth moments of the number of satisfying assignments and overlap between satisfying assignments. We show that for K ? 4 the average overlap between satisfying assignments undergoes a discontinues (first order) transition from a low to high overlap of satassignments. This transition occurs at a value of ff which is just below the numerically observed critical value. Similar, higher order, transition occur for higher moments of the distribution for larger K. The transition in the overlap is observed numerically even for N ß 20. 1 Introduction