2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210567We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to prove them have had many other consequences.Computational Complexity68Q10, 68Q15, 68Q17, 68Q25F.1text