The fast parallel algorithm for CNF SAT without algebra

TL;DR

This paper introduces a novel parallel algorithm for solving CNF SAT problems that avoids algebra and traditional search strategies, achieving linear complexity relative to the number of clauses.

Contribution

The paper presents a linear, parallel, object-oriented SAT solving algorithm that improves efficiency by tracking unsatisfactory binary values, without using algebra or classical search methods.

Findings

Algorithm is linear in the number of clauses.

Efficiency is improved by tracking tested binary values.

Complexity is bounded by 2^n iterations, with n variables.

Abstract

A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies such as branch and bound, back-forward, tree representation, etc. The method is based on the special class of SAT problems, Simple SAT (SSAT). The algorithm's design includes parallel execution, object oriented, and short termination as my previous versions but it keep track of the tested unsatisfactory binary values to improve the efficiency and to favor short termination. The resulting algorithm is linear with respect to the number of clauses plus a process data on the partial solutions of the subproblems SSAT of an arbitrary SAT and it is bounded by $2^{n}$ iterations where $n$ is the number of logical variables. The novelty for the solution of arbitrary SAT problems is a linear algorithm, such its complexity is less or equal than the algorithms of the state of the art for solving SAT.