On Time Versus Space

Abstract

It is shown that every deterministic multitape Turing machine of time complexity t(n) can be simulated by a deterministic Turing machine of tape complexity t(n)/logt(n). Consequently, for tape constructable t(n), the class of languages recognizable by multitape Turing machines of time complexity t(n) is strictly contained in the class of languages recognized by Turing machines of tape complexity t(n). In particular the context-sensitive languages cannot be recognized in linear time by deterministic multitape Turing machines. © 1977, ACM. All rights reserved.