Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 16, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Andreas Galanis (University of Oxford)

Counting solutions in the random k-SAT model

We 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 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))2logk/k, the Gibbs uniqueness threshold for the model. Instead, our algorithm harnesses a recent technique by Moitra to work for random formulas. The main challenge in our setting is to account for the presence of high-degree variables whose marginal distributions are hard to control and which cause significant correlations within the formula.

This is joint work with Leslie Ann Goldberg, Heng Guo, and Kuan Yang.

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