2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141696In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set E(A) containing propositional calculus formulae, each of which requires the algorithm A to take non-polynomial time to find the truth-values of its propositional letters satisfying it. Moreover, E(A)'s size is an exponential function of n, which makes it impossible to detect such formulae in a polynomial time. Hence, the satisfability problem does not have a polynomial complexityComputational ComplexityLogic in Computer ScienceF.1.3text