2024/02/12 by Robert Quigley, Quigley, Robert
Computer Science · #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #F.2.2 #FOS: Computer and information sciences #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2406.08489
openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that any two clauses in an instance of 3SAT sharing the same terminal which is positive in one clause and negated in the other can imply a new clause composed of the remaining terms from both clauses. Clauses can also imply other clauses as long as all the terms in the implying clauses exist in the implied clause. It is shown an instance of 3SAT is unsatisfiable if and only if it can derive contradicting 1-terminal clauses in exponential time. It is further shown that these contradicting clauses can be implied with the aforementioned techniques without processing clauses of length 4 or greater, reducing the computation to polynomial time. Therefore there is a polynomial time algorithm that will produce contradicting 1-terminal clauses if and only if the instance of 3SAT is unsatisfiable. Since such an algorithm exists and 3SAT is NP-Complete, P = NP.