CCF: AF Analytical Tools for Natural Algorithms

Princeton University, Princeton NJ

Investigators

Abstract

This project seeks to build an algorithmic foundation for the analysis of complex self-organizing systems. Computing theory has been successful at pinning down the computational power of common dynamical systems, but less so at analyzing their behavior and functionality. Recent research points to the potential benefits of viewing these systems as "natural algorithms." The approach is premised on the belief that the algorithm itself is at least as important as the data it generates and that the current reliance on simulations and statistics must 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 lay the foundations of an algorithmic theory of complex adaptive systems. Algorithm design has been one of the most fruitful areas of computer science in the past few decades. Building a bridge between this intellectual discipline and the ever-growing area of complex systems could potentially have a major impact on science as a whole. Accordingly, the present project will involve collaborations with computer scientists, control theorists, physicists, and systems biologists.