Ecological Turing Machines

Abstract

The goal of this paper is to investigate the power of Turing machines with homogeneous memory. The standard models of Turing machines often use tricks such as “special” symbols (delimiter) or several different tapes. These tricks are not natural: computers use only 0’s and 1’s and operating systems consider memory as a whole. When memory is divided into several parts, (e.g. hard disks, devices...) they play the same role and we cannot say that one of them is devoted to input while the rest is a working space.

We address the question of computing power of variants of Turing machines with no delimiter, and also investigate how a Turing machine is forced to transform its environment while computing. For this last question, we consider the rest of its tape as an oracle and see whether it is possible to compute all recursive functions relativized to this oracle. If yes it means that, in the considered model, Turing machines can perform computations without destroying their environment (the model is thus called ecological), otherwise computing implies environment transformation.

These problems seem at first sight straightforward but they are not. We could prove 4 main results explained below, but some very simple and intuitive models are yet not clear (we do not know if they are as powerful as standard Turing machines).