The Relative Exponential Time Complexity of Approximate Counting Satisfying Assignments

TL;DR

This paper investigates the exponential time complexity of approximately counting satisfying assignments of CNFs, establishing a reduction to SAT that preserves complexity and introducing a new hypercontractive inequality for analysis.

Contribution

It introduces a reduction from approximate counting to SAT that maintains exponential complexity and presents a new hypercontractive inequality for analysis.

Findings

Reduction preserves exponential complexity of approximate counting

Algorithm performs well in practice with known approximation guarantees

New hypercontractive inequality aids in analysis

Abstract

We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also preserves the exponential complexity of approximate counting. Our algorithm is also similar to an algorithm which works particular well in practice for which however no approximation guarantee was known. Towards an analysis of our reduction we provide a new inequality similar to the Bonami-Beckner hypercontractive inequality.