Foundations of Generalized Reversible Computing

摘要

Information loss from a computation implies energy dissipation due to Landauer's Principle. Thus, increasing the amount of useful computational work that can be accomplished within a given energy budget will eventually require increasing the degree to which our computing technologies avoid information loss, i.e., are logically reversible. But the traditional definition of logical reversibility is actually more restrictive than is necessary to avoid information loss and energy dissipation due to Landauer's Principle. As a result, the operations that have traditionally been viewed as the atomic elements of reversible logic, such as Toffoli gates, are not really the simplest primitives that one can use for the design of reversible hardware. Arguably, a complete theoretical framework for reversible computing should provide a more general, parsimonious foundation for practical engineering. To this end, we use a rigorous quantitative formulation of Landauer's Principle to develop the theory of Generalized Reversible Computing (GRC), which precisely characterizes the minimum requirements for a computation to avoid information loss and the consequent energy dissipation, showing that a much broader range of computations are, in fact, reversible than is acknowledged by traditional reversible computing theory. This paper summarizes the foundations of GRC theory and briefly presents a few of its applications.