Theory of Reversible Computing pp 157-172 | Cite as

# Making Reversible Turing Machines from Reversible Primitives

## Abstract

The problem how we can construct reversible Turing machines (RTMs) out of reversible primitives is investigated. It is shown that any one-tape two-symbol RTM can be concisely realized as a completely garbage-less reversible logic circuit composed of a rotary element (RE), or a reversible logic element with memory RLEM 4-31. Though we deal with only one-tape two-symbol RTMs in the quintuple form for simplicity, the construction method can be generalized for any type of RTMs. Here, an RTM is decomposed into a finite control module, and memory cells. Then, they are implemented as reversible sequential machines (RSMs) using RE or RLEM 4-31. The design methods employed here are quite different from those in the traditional design theory of logic circuits based on logic gates. Furthermore, since RE and RLEM 4-31 have simple realizations in the billiard ball model (BBM), an idealized reversible physical model, the constructed RTMs are further embeddable in BBM.

## Keywords

reversible Turing machine reversible logic element with memory rotary element reversible logic circuit## Preview

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