Survey on the structure of Boolean satisfiability problem

Abstract

P versus NP is a popular conjecture in Computer science. In this conjecture P stands for the problem for which there exists a polynomial time running algorithm and NP stands for the problems for which there exists a nondeterministic polynomial time algorithm. P ?= NP is the conjecture where we have to answer the question of whether there exists a polynomial time running algorithm for all NP problems or not. This thesis presents a comprehensive survey of the Boolean Satisfiability Problem (SAT), a cornerstone of theoretical computer science and practical applications in various domains. We explore the fundamental aspects of SAT, including its historical development, theoretical significance, and the progression of algorithms designed to solve it. The survey encompasses classic approaches such as the Davis-Putnam-Logemann-Loveland (DPLL) algorithm and modern advancements like Conflict-Driven Clause Learning (CDCL) solvers.