Reversible Logic Elements with Memory and Their Universality

K. Morita
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引用次数: 1

Abstract

Reversible computing is a paradigm of computation that reflects physical reversibility, one of the fundamental microscopic laws of Nature. In this survey, we discuss topics on reversible logic elements with memory (RLEM), which can be used to build reversible computing systems, and their universality. An RLEM is called universal, if any reversible sequential machine (RSM) can be realized as a circuit composed only of it. Since a finite-state control and a tape cell of a reversible Turing machine (RTM) are formalized as RSMs, any RTM can be constructed from a universal RLEM. Here, we investigate 2-state RLEMs, and show that infinitely many kinds of non-degenerate RLEMs are all universal besides only four exceptions. Non-universality of these exceptional RLEMs is also argued.
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具有记忆的可逆逻辑元件及其通用性
可逆计算是一种反映物理可逆性的计算范式,这是自然的基本微观定律之一。本文讨论了可用于构建可逆计算系统的可逆存储逻辑元件(RLEM)及其通用性。如果任何可逆顺序机(RSM)都可以实现为仅由可逆顺序机组成的电路,则称为通用可逆顺序机。由于可逆图灵机(RTM)的有限状态控制和磁带单元被形式化为rsm,因此任何RTM都可以由通用RLEM构造。本文研究了二态rlem,并证明了无穷多种非简并rlem除四种例外外都是全称的。本文还讨论了这些例外rlem的非普适性。
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