Counting solutions to random cnf formulas
WebNov 16, 2024 · An algorithm to approximately count the number of solutions to a CNF formula Φ when the width is logarithmic in the maximum degree is introduced, which … WebWe give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k-uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < n o(1) and k ≥ 20 log k + 20 log d + 60, the new sampling algorithm runs in close to linear time, and the counting algorithm runs in close …
Counting solutions to random cnf formulas
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Webtitle = "Tinted, Detached, and Lazy CNF-XOR Solving and Its Applications to Counting and Sampling", abstract = "Given a Boolean formula, the problem of counting seeks to estimate the number of solutions of F while the problem of uniform sampling seeks to sample solutions uniformly at random. WebCounting Solutions to Random CNF Formulas Mathematics of computing Discrete mathematics Combinatorics Probability and statistics Theory of computation Design and …
WebNov 16, 2024 · The best previous counting algorithm was due to Montanari and Shah and was based on the correlation decay method, which works up to densities (1+o_k (1))2log k/k, the Gibbs uniqueness threshold for the model. Instead, our algorithm harnesses a recent technique by Moitra to work for random formulas. Webdom CNF-XOR formulas. We empirically demon-strate that a state-of-the-art SAT solver scales ex-ponentially on random CNF-XOR formulas across a wide range of XOR-clause densities, peaking around the empirical phase-transition location. On the theoretical front, we prove that the solution space of a random CNF-XOR formula ‘shatters’
WebCounting solutions to random CNF formulas. A. Galanis, L. A. Goldberg, H. Guo, and K. Yang. SIAM Journal on Computing, 50 (6): 1701-1738, 2024. Preliminary version in ICALP 2024 . arXiv conference journal The complexity of approximating the complex-valued Potts model. A. Galanis, L. A. Goldberg, and A. Herrera-Poyatos. Webcan be applied to the problem of counting the number of solutions to a given propositional SAT formula. 1. Introduction The inclusion-exclusion principle gives a formula for computing the cardi-nality of the union of a collection of sets: j[n i=1 A ij. The formula, expressed as an alternating sum, plays an important role in combinatorics and ...
WebThis work gives the first efficient algorithm to approximately count the number of solutions in the random k-SAT model when the density of the formula scales exponentially with k, using a recent technique by Moitra to work for random formulas with much higher densities. We give the first efficient algorithm to approximately count the number of …
WebCOUNTING SOLUTIONS TO RANDOM CNF FORMULAS ANDREAS GALANIS, LESLIE ANN GOLDBERG, HENG GUO, AND KUAN YANG Abstract. We give the first efficient … found sw-dp with id 0x0bc11477WebThis work gives the first efficient algorithm to approximately count the number of solutions in the random k-SAT model when the density of the formula scales exponentially with k, … disc image to exedisc images iso filesWebNov 16, 2024 · Counting solutions to random CNF formulas Authors: Andreas Galanis Leslie Ann Goldberg Heng Guo Kuan Yang Shanghai Jiao Tong University Abstract We give the first efficient algorithm to... found sw-dp with id 0x0bb11477WebLet Φ = Φ(k,n,m) be a k-CNF formula on nBoolean variables with mclauses chosen uniformlyatrandomwhereeachclausehassizek≥3. TherandomformulaΦ showsan … disc image tools microsoftWebWe give the first efficient algorithm to approximately count the number of solutions in the randomk-SAT model when the density of the formula scales exponentially with k.The … found svocWebWe give the first efficient algorithm to approximately count the number of solutions in the random k -SAT model when the density of the formula scales exponentially with k. The … disc image tools windows 10 iso