English

The Long, the Short and the Random

Computational Complexity 2020-11-10 v2 Artificial Intelligence Discrete Mathematics Data Structures and Algorithms

Abstract

We furnish solid evidence, both theoretical and empirical, towards the existence of a deterministic algorithm for random sparse #Ω(logn)\#\Omega(\log n)-SAT instances, which computes the exact counting of satisfying assignments in sub-exponential time. The algorithm uses a nice combinatorial property that every CNF formula has, which relates its number of unsatisfying assignments to the space of its monotone sub-formulae.

Keywords

Cite

@article{arxiv.2011.01649,
  title  = {The Long, the Short and the Random},
  author = {Giorgio Camerani},
  journal= {arXiv preprint arXiv:2011.01649},
  year   = {2020}
}

Comments

18 pages, 10 figures. Software implementation (in Java) available for download

R2 v1 2026-06-23T19:52:58.185Z