Analog computation with continuous ODEs

Abstract

Demonstrates simple, low-dimensional systems of ODEs that can simulate arbitrary finite automata, push-down automata, and Turing machines. We conclude that there are systems of ODEs in R/sup 3/ with continuous vector fields possessing the power of universal computation. Further, such computations can be made robust to small errors in coding of the input or measurement of the output. As such, they represent physically realizable computation. We make precise what we mean by "simulation" of digital machines by continuous dynamical systems. We also discuss elements that a more comprehensive ODE-based model of analog computation should contain. The "axioms" of such a model are based on considerations from physics.<>