Paper Abstract and Keywords |
Presentation |
2008-10-10 15:15
Size-Energy Tradeoff for Threshold Logic Circuits Computing MOD Functions Kei Uchizawa (Tohoku Univ.), Eiji Takimoto (Kyushu Univ.), Takao Nishizeki (Tohoku Univ.) COMP2008-42 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
A threshold logic circuit $C$ computing a Boolean function MOD$_m: \{ 0,1\}^n \to \{0, 1\}$ outputs ``0'' if the number of ones in the input $\Vec{x}\in \{0, 1\}^n$ to $C$ is a multiple of $m$ and,otherwise,$C$ outputs ``1'', where $n \ge 1$ and $m\ge 2$. The function MOD$_2$ is the so-called parity function. Let $s$ be the size of the circuit $C$, that is, $C$ consists of $s$ threshold gates, and let $e$ be the energy complexity of $C$, that is, at most $e$ gates in $C$ output ``1'' for any input $\Vec{x} \in \{ 0, 1\}^n$ when $C$ computes MOD$_m$. In the paper, we prove that $n/(m-1) \le s^e$ for every circuit $C$ computing MOD$_m$. Both $n$ and $m$, and hence $n/(m-1)$, do not depend on the design of $C$. On the other hand, $s$ and $e$ depend on the design of $C$, and $s^e$ is monotonically increasing with respect to $s$ and $e$. Therefore, the inequality $n/(m-1) \le s^e$ implies that there is a tradeoff between size $s$ and energy complexity $e$ of a threshold circuit $C$ computing MOD$_m$. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Threshold circuit / Energy complexity / size / MOD function / Parity function / Circuit complexity / Boolean function / |
Reference Info. |
IEICE Tech. Rep., vol. 108, no. 237, COMP2008-42, pp. 63-69, Oct. 2008. |
Paper # |
COMP2008-42 |
Date of Issue |
2008-10-03 (COMP) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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COMP2008-42 |
Conference Information |
Committee |
COMP |
Conference Date |
2008-10-10 - 2008-10-10 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Tohoku Univ. |
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(See Japanese page) |
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Paper Information |
Registration To |
COMP |
Conference Code |
2008-10-COMP |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Size-Energy Tradeoff for Threshold Logic Circuits Computing MOD Functions |
Sub Title (in English) |
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Threshold circuit |
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Energy complexity |
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size |
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MOD function |
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Parity function |
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Circuit complexity |
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Boolean function |
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1st Author's Name |
Kei Uchizawa |
1st Author's Affiliation |
Tohoku University (Tohoku Univ.) |
2nd Author's Name |
Eiji Takimoto |
2nd Author's Affiliation |
Kyushu University (Kyushu Univ.) |
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Takao Nishizeki |
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Tohoku University (Tohoku Univ.) |
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Speaker |
Author-1 |
Date Time |
2008-10-10 15:15:00 |
Presentation Time |
30 minutes |
Registration for |
COMP |
Paper # |
COMP2008-42 |
Volume (vol) |
vol.108 |
Number (no) |
no.237 |
Page |
pp.63-69 |
#Pages |
7 |
Date of Issue |
2008-10-03 (COMP) |
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