The #ETH is False, #k-SAT is in Sub-Exponential Time

TL;DR

This paper presents a randomized algorithm for #k-SAT that counts solutions in sub-exponential time, challenging the widely held ETH and related hypotheses in computational complexity.

Contribution

It introduces a novel randomized algorithm for #k-SAT with sub-exponential runtime, refuting the #ETH and several other complexity hypotheses.

Findings

Existence of a #k-SAT counting algorithm in 2^{o(n)} time

Refutation of #ETH, ETH, #SETH, and related hypotheses

Implications for complexity theory and problem hardness

Abstract

We orchestrate a randomized algorithm for #$k$-SAT which counts the exact number of satisfying assignments in $2^{o(n)}$ time. The existence of such algorithm signifies that the #ETH is hereby refuted, and so are $\oplus$ETH, ETH, #SETH, $\oplus$SETH and SETH.