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Title:
Approximate counting and the Lovasz local lemma
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Abstract:
We introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Moreover our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random.
Our program is a significant departure from earlier techniques in approximate counting, and is a based on a framework to bootstrap an oracle for computing marginal probabilities on individual variables.
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