Inexact computing also referred to as approximate computing is a style of designing algorithms and computing systems wherein the accuracy of correctness of algorithms executing on them is deliberately traded for significant resource savings. Significant progress has been reported in this regard both in terms of hardware as well as software or custom algorithms that exploited this approach resulting in some loss in solution quality (accuracy) while garnering disproportionately high savings. However, these approaches tended to be ad-hoc and were tied to specific algorithms and technologies. Consequently, a principled approach to designing and analyzing algorithms was lacking. In this paper, we provide a novel model which allows us to characterize the behavior of algorithms designed to be inexact, as well as characterize opportunities and benefits that this approach offers. Our methods therefore are amenable to standard asymptotic analysis and provides a clean unified abstraction through which an algorithm's design and analysis can be conducted. With this as a backdrop, we show that inexactness can be significantly beneficial for some fundamental problems in that the quality of a solution can be exponentially better if one exploits inexactness when compared to approaches that are agnostic and are unable to exploit this approach. We show that such gains are possible in the context of evaluating Boolean functions rooted in the theory of Boolean functions and their spectra, PAC learning, and sorting. Formally, this is accomplished by introducing the twin concepts of inexactness aware and inexactness oblivious approaches to designing algorithms and the exponential gains are shown in the context of taking the ratio of the quality of the solution using the "aware" approach to the "oblivious" approach.

翻译：非精确计算（亦称近似计算）是一种算法与计算系统的设计范式，其核心在于有意识地牺牲算法执行的正确性精度，以换取显著的资源节约。目前，无论是硬件层面，还是利用该方法实现的软件或定制算法，均已取得重要进展——虽导致解质量（精度）的有限损失，却能获得不成比例的高效收益。然而，这些方法往往具有临时性，且紧密依赖特定算法与技术。因此，领域内长期缺乏一种具备原则性的算法设计与分析方法。本文提出一种新颖模型，既能刻画非精确算法的行为特性，也可量化该方法带来的机遇与效益。我们的方法兼容标准渐近分析框架，并提供清晰统一的抽象层，使算法的设计与分析得以系统化展开。以此为基础，我们证明非精确性对某些基本问题具有显著优势：相较于无法利用非精确性的无感知方法，通过主动利用非精确性，解的质量可实现指数级提升。我们通过三类场景验证此类增益：基于布尔函数及其谱理论的布尔函数求值、PAC学习以及排序问题。从形式化角度，我们引入"非精确感知"与"非精确无感知"这对孪生概念来设计算法，并通过计算"感知方法"与"无感知方法"的解质量比值，论证指数级增益的存在性。