CCF: AF Analytical Tools for Natural Algorithms

这个项目试图为分析复杂的自组织系统建立一个算法基础。计算理论已经成功地限制了普通动力系统的计算能力，但在分析它们的行为和功能方面还不是很成功。最近的研究指出了将这些系统视为“自然算法”的潜在好处。这种方法的前提是相信算法本身至少和它产生的数据一样重要，而且目前对模拟和统计的依赖必须得到分析工具的补充，类似于“算法演算”。这项研究将沿着以下路线进行：新的证明技术和分析工具；基于通信的算法重整化；复杂系统的几何学、拓扑学和近似性。本项目的目标是为复杂适应系统的算法理论奠定基础。在过去的几十年里，算法设计一直是计算机科学中最有成果的领域之一。在这一智能学科和不断增长的复杂系统领域之间建立一座桥梁，可能会对整个科学产生重大影响。因此，本项目将涉及与计算机科学家、控制理论家、物理学家和系统生物学家的合作。

This project seeks to build an algorithmic foundationfor the analysis of complex self-organizing systems.Computing theory has been successful atpinning down the computational power ofcommon dynamical systems, but less soat analyzing their behavior and functionality.Recent research points to the potential benefitsof viewing these systems as "natural algorithms."The approach is premised on the belief thatthe algorithm itself is at least as importantas the data it generates and thatthe current reliance on simulations and statisticsmust be supplemented with analytical tools,something akin to an ``algorithms calculus.''The research will be oriented along the following lines:new proof techniques and analytical tools;communication-based algorithmic renormalization;geometry, topology, and approximation of complex systems.The ambition of this project is to laythe foundations of an algorithmic theory ofcomplex adaptive systems. Algorithm designhas been one of the most fruitfulareas of computer science in the past few decades.Building a bridge between this intellectual disciplineand the ever-growing area of complex systemscould potentially have a major impact on science as a whole.Accordingly, the present project will involvecollaborations with computer scientists, control theorists,physicists, and systems biologists.