Home
Hostname: page-component-99c86f546-md8df Total loading time: 0.378 Render date: 2021-12-04T20:06:59.135Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

# 11 - Circuit Complexity

## from Part IV - Graph Representations and Efficient Computation Models

Published online by Cambridge University Press:  05 June 2013

By
Edited by

## Summary

Introduction

The theory on efficient algorithms and complexity theory is software oriented. Their hardware-oriented counterpart is the theory on combinational circuits or, simply, circuits. The main difference is that circuits are a nonuniform model. A circuit is designed for one Boolean function f Є Bn,m, that is, f: {0, 1}n → {0, 1}m. However, most circuit designs lead to sequences of circuits realizing a sequence of functions. Typical adders are sequences of adders, one for each input length. If there is an efficient algorithm computing for each n the circuit for input length n, the circuit family is called uniform. However, for basic functions like arithmetic functions or storage access the circuit model is more adequate than software models. Moreover, circuits are a very simple and natural computation model reflecting all aspects of efficiency.

A circuit model needs a basis of elementary functions that can be realized by simple gates. In the basic circuitmodel, a basis is a finite set. Then a circuit for input size n is a finite sequence of instructions or gates and, therefore, a straight-line program: the ith instruction consists of a function g from the chosen basis and, if g Є Bj ≔ Bj,1, a sorted list Ii,1, …, Ii, j of inputs. The constants 0 and 1, the variables x1, …, xn, and the results r1, …, ri–1 of the first i – 1 instructions are possible inputs.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

## Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

### Purchase

Buy print or eBook[Opens in a new window]

# Send book to Kindle

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

# Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

# Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×