Nondeterministic Time and Space Complexity Classes

Abstract

The marginal utility of the Turing machine computational resources running time and storage space are studied. A technique is developed which, unlike diagonalization, applies equally well to nondeterministic and deterministic automata. For f, g time or space bounding functions with f (n+1) small compared to g(n), it is shown that, in terms of word length n, there are languages which are accepted by Turing machines operating within time or space g(n) but which are accepted by no Turing machine operating within time or space f(n). The proof involves use of the recursion theorem together with "padding" or "translational" techniques of formal language theory.