Reversible Turing Machines

Abstract

A reversible Turing machine (RTM) is a basic model for studying computational universality, and computational complexity in reversible computing. In this chapter, after giving definitions on RTMs, we explain the method of Bennett for constructing a three-tape RTM that simulates a given irreversible TM. By this, computational universality of the class of three-tape RTMs is derived. We then clarify basic properties of RTMs, and study several variations of RTMs. In particular, we give simplification methods for RTMs. They are methods for reducing the number of tapes, the number of tape symbols, and the number of states of RTMs. From them, the computational universality of one-tape two-symbol RTMs with one-way infinite tape, and one-tape three state RTMs is derived. These results are useful for showing the computational universality of other reversible systems, and for composing reversible computing machines out of reversible logic elements.

Keywords