A New Approach to CNF-SAT From a Probabilistic Point of View (2104.11233v1)

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.