Making Reversible Turing Machines from Reversible Primitives
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.
Keywordsreversible Turing machine reversible logic element with memory rotary element reversible logic circuit
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