2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112307Proving lower bounds remains the most difficult of tasks in computational complexity theory. In this paper, we show that whereas most natural NP-complete problems belong to NLIN (linear time on nondeterministic RAMs), some of them, typically the planar versions of many NP-complete problems are recognized by nondeterministic RAMs in linear time and sublinear space. The main results of this paper are the following: as the second author did for NLIN, we give exact logical characterizations of nondeterministic polynomial time-space complexity classes; we derive from them a class of problems, which are complete in these classes, and as a consequence of such a precise result and of some recent separation theorems using diagonalization, prove time-space lower bounds for these problems.19 pages, 4 figuresComputational ComplexityLogic in Computer ScienceF.1.3; F.4.1text