Two heads are better than two tapes
Computational Complexity
2007-05-23 v1
Abstract
We show that a Turing machine with two single-head one-dimensional tapes cannot recognize the set {x2x'| x \in {0,1}^* and x' is a prefix of x} in real time, although it can do so with three tapes, two two-dimensional tapes, or one two-head tape, or in linear time with just one tape. In particular, this settles the longstanding conjecture that a two-head Turing machine can recognize more languages in real time if its heads are on the same one-dimensional tape than if they are on separate one-dimensional tapes.
Cite
@article{arxiv.cs/0110039,
title = {Two heads are better than two tapes},
author = {Tao Jiang and Joel Seiferas and Paul Vitanyi},
journal= {arXiv preprint arXiv:cs/0110039},
year = {2007}
}
Comments
LaTeX, 16 pages. The final journal paper contains minor corrections as well as some extra typos, but, also, some clarifying figures. A close copy to that can be downloaded from http://www.cwi.nl/~paulv/complexity.html