Publication Date



Technical Report: UTEP-CS-18-71


Ladner's 1975 result says that any NP-complete problem -- i.e., in effect, any maximally complex problem -- can be reduced to solving two easier problems. This result sounds counter-intuitive: if a problem is maximally complex, how can it be reduced to simpler ones? In this paper, we provide an intuitive explanation for this result. Our main argument is that since complexity and easiness-to-divide are not perfectly correlated, it is natural to expect that maximally complex problem is not maximally difficult to divide. Our related argument is that -- as this result shows -- NP-completeness is a sufficient but not a necessary condition for a problem to be maximally complex; how to come up with a more adequate notion of complexity is still an open problem.