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Related Terms and Synonyms . . . . . . . . . . . . . . . . . . Similar yet Unrelated Concepts . . . . . . . . . . . . . . . . . 1 Notions of Computing 3 4 5 7 Consider the word computation. For some strange and unknown reason, the notion that naturally arises in one’s mind is that of forward computation. The unidirectionality of computational flow seems to be the natural and intuitive notion for many people. Even more interestingly, no notion of computation in the opposite direction seems to be naturally triggered in one’s mind—neither a mental model nor even a recollection of any related reversible phenomenon.

This ability to pause the forward or backward execution at any point and the ability to switch the direction of execution is the generalized challenge of reversible computing. Specific variants and specializations of this general reversible computing problem arise in different contexts. Historically, low power computing has been a major motivating factor behind the development of reversible computing. Over time, additional areas have emerged in which reversible computing has found applications.

Given that the bit erasures form the sole cause of irrecoverable energy consumption, the important question that follows is whether every computation can be performed without bit erasures. This question was answered in the positive by introducing reversible computing. A notion of the reverse of any computation is introduced, which is then used in a higher-level algorithm to accomplish any computation without bit erasures (see Chapter 4 and Chapter 6). In this way, the reduction and recycling of energy is one of the fundamental applications of reversible computing, holding far-reaching potential in the future of computing.

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An algebra lemma by Brian Osserman

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