Relaxed Random Search for Solving K-Satisfiability and its Information Theoretic Interpretation

Abstract

Abstract-The problem of finding satisfying assignments for conjunctive normal formula with K literals in each clause, known as K-SAT, has attracted many attentions in the previous three decades. Since it is known as NP-Complete Problem, its effective solution (finding solution within polynomial time) would be of great interest due to its relation with the most well-known open problem in computer science (P=NP Conjecture). Different strategies have been developed to solve this problem but in all of them the complexity is preserved in NP class. In this paper, by considering the recent approach of applying statistical physic methods for analyzing the phase transition in the complexity of algorithms used for solving K-SAT, we try to compute the complexity of using randomized algorithm for finding the solution of K-SAT in more relaxed regions. It is shown how the probability of literal flipping process can change the complexity of algorithm substantially. An information theoretic interpretation of this reduction in time complexity will be argued.