Analog computation with continuous ODEs

Author

Branicky, Michael S.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

fYear

1994

fDate

17-20 Nov 1994

Firstpage

265

Lastpage

274

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 R³ 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

Keywords

Turing machines; analogue simulation; coding errors; differential equations; finite automata; measurement errors; pushdown automata; vectors; Turing machines; analog computation; axioms; continuous dynamical systems; continuous ordinary differential equations; continuous vector fields; digital machines; finite automata; input coding error robustness; low-dimensional systems; output measurement error robustness; physically realizable computation; physics; push-down automata; simulation; universal computation; Analog computers; Automata; Computational modeling; Computer networks; Computer science; Computer simulation; Neural networks; Physics computing; Power measurement; Robustness;

fLanguage

English

Publisher

ieee

Conference_Titel

Physics and Computation, 1994. PhysComp '94, Proceedings., Workshop on

Conference_Location

Dallas, TX

Print_ISBN

0-8186-6715-X

Type

conf

DOI

10.1109/PHYCMP.1994.363672

Filename

363672