Deterministic Simulation of a Single Tape Turing Machine by a Random Access Machine in Sub-linear Time

Turing machines which use a single tape both for their input and as their only working space (known as 1TTMs) appear to be extremely slow for many problems compared with multi-tape Turing machines and Random Access Machines (RAMS). However, apart from a few simple problems which require quadratic time on a 1TTM but have simple linear time solutions on a multi-tape Turing machine, there have been no general results proving this appearance to be correct. Indeed when the time for a RAM is reckoned by the reasonable logarithmic cost criterion (Aho et al., 1974; Cook and Reckhow, 1973), which will be adopted throughout this paper, it is not immediately obvious that all problems can be solved as fast on a RAM as on a 1TTM.