Paper Abstract and Keywords |
Presentation |
2010-01-25 16:10
Size-Energy Tradeoff of Unate Circuits Computing Symmetric Functions Kei Uchizawa (Tohoku Univ.), Eiji Takimoto (Kyushu Univ.), Takao Nishizeki (Tohoku Univ.) COMP2009-47 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
A unate gate is a logical gate computing a unate Boolean function.
Examples of unate gates are
AND-gates, OR-gates, NOT-gates, threshold gates, \emph{etc}.
A unate circuit $C$ is a combinatorial logic circuit
consisting of unate gates.
Let $f$ be a symmetric
Boolean function of $n$ variables, whose value depends only on the number of ones
in the input.
Let $m_0$ and $m_1$ be the maximum number of consecutive 0's and consecutive 1's in the
value vector of $f$, respectively, and let $l=\min \{ m_0, m_1\}$ and $m=\max\{ m_0, m_1\}$.
Let $C$ be a unate circuit computing $f$.
Let $s$ be the size of the circuit $C$,
that is, $C$ consists of $s$ gates.
Let $e$ be the energy of $C$,
that is, at most $e$ gates in $C$ output ``1'' for any input.
In the paper, we show that there is a tradeoff between the size $s$ and energy $e$ of $C$.
More precisely, we show that $(n+1-l)/m \le s^e$.
We also present lower bounds on the size $s$ of $C$ represented in terms of $n$, $l$ and $m$.
Our tradeoff immediately implies that
$\log n\le e \log s$
for every unate circuit $C$ computing the Parity function of $n$
variables. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Unate circuit / Energy complexity / Size / Circuit complexity / Symmetric function / Boolean function / / |
Reference Info. |
IEICE Tech. Rep., vol. 109, no. 391, COMP2009-47, pp. 57-64, Jan. 2010. |
Paper # |
COMP2009-47 |
Date of Issue |
2010-01-18 (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) |
Download PDF |
COMP2009-47 |
Conference Information |
Committee |
COMP |
Conference Date |
2010-01-25 - 2010-01-25 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Nishijin Plaza, Kyushu University |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
|
Paper Information |
Registration To |
COMP |
Conference Code |
2010-01-COMP |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Size-Energy Tradeoff of Unate Circuits Computing Symmetric Functions |
Sub Title (in English) |
|
Keyword(1) |
Unate circuit |
Keyword(2) |
Energy complexity |
Keyword(3) |
Size |
Keyword(4) |
Circuit complexity |
Keyword(5) |
Symmetric function |
Keyword(6) |
Boolean function |
Keyword(7) |
|
Keyword(8) |
|
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.) |
3rd Author's Name |
Takao Nishizeki |
3rd Author's Affiliation |
Tohoku University (Tohoku Univ.) |
4th Author's Name |
|
4th Author's Affiliation |
() |
5th Author's Name |
|
5th Author's Affiliation |
() |
6th Author's Name |
|
6th Author's Affiliation |
() |
7th Author's Name |
|
7th Author's Affiliation |
() |
8th Author's Name |
|
8th Author's Affiliation |
() |
9th Author's Name |
|
9th Author's Affiliation |
() |
10th Author's Name |
|
10th Author's Affiliation |
() |
11th Author's Name |
|
11th Author's Affiliation |
() |
12th Author's Name |
|
12th Author's Affiliation |
() |
13th Author's Name |
|
13th Author's Affiliation |
() |
14th Author's Name |
|
14th Author's Affiliation |
() |
15th Author's Name |
|
15th Author's Affiliation |
() |
16th Author's Name |
|
16th Author's Affiliation |
() |
17th Author's Name |
|
17th Author's Affiliation |
() |
18th Author's Name |
|
18th Author's Affiliation |
() |
19th Author's Name |
|
19th Author's Affiliation |
() |
20th Author's Name |
|
20th Author's Affiliation |
() |
Speaker |
Author-1 |
Date Time |
2010-01-25 16:10:00 |
Presentation Time |
35 minutes |
Registration for |
COMP |
Paper # |
COMP2009-47 |
Volume (vol) |
vol.109 |
Number (no) |
no.391 |
Page |
pp.57-64 |
#Pages |
8 |
Date of Issue |
2010-01-18 (COMP) |
|