A New Approach to CNF-SAT From a Probabilistic Point of View

TL;DR

This paper introduces a probabilistic approach to CNF-SAT problems, proposing an algorithm that can potentially reduce exponential complexity and provide new insights into satisfiability analysis.

Contribution

It presents a novel probabilistic method for CNF-SAT that may improve efficiency and offers new theoretical insights into logical satisfiability.

Findings

Probabilistic approach can reduce exponential complexity in some cases

New properties derived from probability theory aid in satisfiability analysis

Algorithm shows improved speed for certain CNF formulas

Abstract

The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT) in some cases. It is known that any (CNF) formula is solved with a time complexity of $2^n$ where n is the number of different literals in the (CNF) formula. In our approach, we will follow an enhanced method from a probabilistic point of view that does not always increase exponentially with the number of different literals. This will enhance the chance of determining whether a large formula is satisfiable or not in many cases. Additionally, we will point out at some promising properties that follow from applying probability theory concepts and axioms to logic, which might originate more insights about the satisfiability of logical formulas.