A Faster Exact Algorithm to Count X3SAT Solutions

07/15/2020
by   Gordon Hoi, et al.
0

The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are set to 0. If we restrict the length of each clause to be at most 3 literals, then it is known as the X3SAT problem. In this paper, we consider the problem of counting the number of satisfying assignments to the X3SAT problem, which is also known as #X3SAT. The current state of the art exact algorithm to solve #X3SAT is given by Dahllöf, Jonsson and Beigel and runs in O(1.1487^n), where n is the number of variables in the formula. In this paper, we propose an exact algorithm for the #X3SAT problem that runs in O(1.1120^n) with very few branching cases to consider, by using a result from Monien and Preis to give us a bisection width for graphs with at most degree 3.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/08/2020

An Improved Exact Algorithm for the Exact Satisfiability Problem

The Exact Satisfiability problem, XSAT, is defined as the problem of fin...
research
01/10/2018

Deterministic search for CNF satisfying assignments in almost polynomial time

We consider the fundamental derandomization problem of deterministically...
research
01/21/2021

Improved Algorithms for the General Exact Satisfiability Problem

The Exact Satisfiability problem asks if we can find a satisfying assign...
research
05/13/2021

A Fast Algorithm for SAT in Terms of Formula Length

In this paper, we prove that the general CNF satisfiability problem can ...
research
01/10/2021

Learning from Satisfying Assignments Using Risk Minimization

In this paper we consider the problem of Learning from Satisfying Assign...
research
06/14/2021

Exact Counting and Sampling of Optima for the Knapsack Problem

Computing sets of high quality solutions has gained increasing interest ...
research
10/29/2019

Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms

Given a Boolean formula ϕ(x) in conjunctive normal form (CNF), the densi...

Please sign up or login with your details

Forgot password? Click here to reset