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Abstract: We develop efficient deterministic algorithms for approximating the fraction of truth assignments that satisfy a disjunctive normal form formula. Although the algorithms themselves are deterministic, their analysis is probabilistic and uses the notion of limited independence between random variables. International Computer Science Institute, 1947 Center Street, Berkeley, California 94704 and Computer Science Department, UC Berkeley, research partially supported by NSF operating grant... (Update)
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...1 rk = 2. Very hard in general, the problem of counting models turns out to be quite tractable in many practical cases. Luby and Velickovic [22] have presented an algorithm for approximating the number of models of a DNF propositional formula with m clauses on n variables. The...
.... assignments of a boolean formula in DNF form F = 1 C i is an instance of the general problem that had been extensively studied [7]. Here A i is the set of assignments that satisfy C i , and Pr( i2S A i ) a S =2 where i2S C i is satis ed by a S assignments. Judging...
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BibTeX entry: (Update)
M. Luby and B. Velickovic. On deterministic approximation of DNF. In Proceedings of the 23 rd Annual ACM Symposium on Theory of Computing, pages 430--438, May 1991. http://citeseer.ist.psu.edu/article/luby93deterministic.html More
@inproceedings{ luby91deterministic,
author = "Michael Luby and Boban Veli{\v{c}}kovic",
title = "On deterministic approximation of {DNF}",
pages = "430--438",
year = "1991",
url = "citeseer.ist.psu.edu/article/luby93deterministic.html" }
Citations (may not include all citations):251 The complexity of computing the permanent (context) - Valiant - 1979
199 A Simple Parallel Algorithm for the Maximal Independent Set .. (context) - Luby - 1986
138 Small Bias Probability Spaces: Efficient Constructions and A.. - Naor, Naor
128 Simple constructions of almost k-wise independent random var.. - Alon, Goldreich et al.
115 Separating the Polynomial-Time Hierarchy by Oracles (context) - Yao
102 A Fast and Simple Randomized Parallel Algorithm for the Maxi.. (context) - Alon, Babai et al. - 1986
82 Lower bounds on the monotone complexity of some Boolean func.. (context) - Razborov - 1985
68 Hardness vs. Randomness (context) - Nisan, Wigderson
68 Monte-Carlo Approximation Algorithms for Enumeration Problem.. (context) - Luby, Madras - 1989
68 Computational limitations for small depth circuits (context) - Hastad - 1986
58 Monte-Carlo algorithms for enumeration and reliability probl.. (context) - Karp, Luby
45 Parity, Circuits and the Polynomial Time Hierarchy (context) - Furst, Saxe et al.
43 Intersection theorems for systems of sets (context) - Erdos, Rado
40 Approximations of General Independent Distributions - Even, Goldreich et al. - 1992
27 Pseudo-random generators and complexity classes (context) - Boppana, Hirschfeld - 1989
23 Approximate Inclusion-Exclusion - Linial, Nisan
11 Deterministic Simulation of Probabilistic constant depth cir.. (context) - Ajtai, Wigderson
9 Randomness, adversaries and computation (context) - Vazirani - 1986
6 Sur les courbes alg'ebriques et les vari'et'es qui s'en d'ed.. (context) - Weil - 1948
5 P 1 1 -Formulae on Finite Structures (context) - Ajtai - 1983
1 On Deterministic Approximate Counting of Solutions to Polyno.. (context) - Luby, Velickovi'c et al.
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