AF: Small: Noise Across Computational Settings

该项目将扩大我们对噪声的理解，并开发新的工具来应对各种计算环境中的噪声，并从中受益。本项目所考虑的设置可以分为三组：(1)互动交流；(2)电路计算；(3)作为计算设备的动力系统。考虑噪声在每种情况下的影响，会产生许多有趣而重要的问题。在理论层面上，该项目旨在开发在处理使用不可靠组件的计算时的纠错新方案，并绘制出这些方案的局限性。在实际应用中，该研究可能会导致开发更有效的纠错通信方案和更节能的电路。在技术层面上，该提案的交叉主题是使用信息论来更好地理解不同环境下噪声的影响。PI和其他机构在本项目所研究领域的过去工作表明，在这些不同的环境之间将会有技术转让。该项目将多个学科联系在一起：交互式纠错是传统编码理论与通信复杂性之间的一个前沿问题；电路纠错在复杂性理论和计算机体系结构中都很有趣；噪声动力系统的计算方面的研究汇集了理论计算机科学，动力系统和理论物理。该项目的更广泛影响包括课程开发，拓宽学生在理论领域的参与和撰写调查文章。

The project will expand our understanding of noise and develop new tools for coping with, and benefiting from noise in a variety of computational settings. Settings considered under this project can be broken into three groups: (1) interactive communication; (2) circuit computation; and (3) dynamical systems when viewed as computing devices. Considering the effect of noise in each of these settings yields many interesting and important problems. At a theoretical level, the project aims to develop new schemes for error-correction when dealing with computation using unreliable components, as well as to map out the limitations of such schemes. At a practical level, the research may lead to the development of more efficient error-correcting communication schemes, and more power efficient circuits.At a technical level, the cross-cutting theme of this proposal is using information theory to better understand the effect of noise in the different settings. Past work by the PI and others in the areas studied under this project, suggests that there will be a transfer of techniques between these different settings. The project connects several disciplines: interactive error-correction is on the cusp between traditional coding theory and communication complexity; circuit error correction is of interest within both complexity theory and computer architecture; and the study of computational aspects of noisy dynamical systems brings together theoretical computer science, dynamical systems, and theoretical physics. Broader impacts of the project include curriculum development, broaden participation of students in theoretical areas and writing survey articles.