Generic hardness of the Boolean satisfiability problem

Abstract

Abstract It follows from the famous result of Cook about the NP-completeness of the Boolean satisfiability problem that there is no polynomial algorithm for this problem if P ≠ N ⁢ P {P\neq NP} . In this paper, we prove that the Boolean satisfiability problem remains computationally hard on polynomial strongly generic subsets of formulas provided P ≠ N ⁢ P {P\neq NP} and P = B ⁢ P ⁢ P {P=BPP} . Boolean formulas are represented in the natural way by labeled binary trees.