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Analog Computation

  • Reference work entry
Computational Complexity

Article Outline

Glossary

Definition of the Subject

Introduction

Fundamentals of Analog Computing

Analog Computation in Nature

General-Purpose Analog Computation

Analog Computation and the Turing Limit

Analog Thinking

Future Directions

Bibliography

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Notes

  1. 1.

    See MacLennan [45,46] for a more detailed discussion of the frame of relevance of the CT model.

  2. 2.

    See MacLennan [45,46] for a more detailed discussion of the frames of relevance of natural computation and control.

Abbreviations

Accuracy:

The closeness of a computation to the corresponding primary system.

BSS:

The theory of computation over the real numbers defined by Blum, Shub, and Smale.

Church–Turing (CT) computation:

The model of computation based on the Turing machine and other equivalent abstract computing machines; commonly accepted as defining the limits of digital computation.

EAC:

Extended analog computer defined by Rubel.

GPAC:

General-purpose analog computer.

Nomograph:

A  device for the graphical solution of equations by means of a family of curves and a straightedge.

ODE:

Ordinary differential equation.

PDE:

Partial differential equation.

Potentiometer:

A variable resistance, adjustable by the computer operator, used in electronic analog computing as an attenuator for setting constants and parameters in a computation.

Precision:

The quality of an analog representation or computation, which depends on both resolution and stability.

Primary system:

The system being simulated, modeled, analyzed, or controlled by an analog computer, also called the target system.

Scaling:

The adjustment, by constant multiplication, of variables in the primary system (including time) so that the corresponding variables in the analog systems are in an appropriate range.

TM:

Turing machine.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering & Computer Science, University of Tennessee, Knoxville, USA

    Bruce J. MacLennan

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  1. Bruce J. MacLennan
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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MacLennan, B.J. (2012). Analog Computation. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_12

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