| Paper Abstract and Keywords |
| Presentation |
2006-06-23 11:10
Reductions for Monotone Boolean Circuits
Kazuo Iwama, Hiroki Morizumi (Kyoto Univ.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
The large class, say {\it NLOG}, of Boolean functions, including 0-1 Sort and 0-1 Merge, have an upper bound of $O(n\log n)$ for their monotone circuit size, i.e., have circuits with $O(n\log n)$ AND/OR gates of fan-in two. Suppose that we can use, besides such normal AND/OR gates, any number of more powerful ``$F$-gates'' which realize a monotone Boolean function $F$ with $r (\geq 2)$ inputs and $r' (\geq 1)$ outputs. Note that the cost of each AND/OR gate is one and we assume that the cost of each $F$-gate is $r$. Now we define: A Boolean function $f$ in NLOG is said to be $F$-Easy if $f$ can be computed by a circuit with AND/OR/$F$ gates whose total cost is $o(n\log n)$. In this paper we show that 0-1 Merge is not $F$-Easy for an arbitrary monotone function $F$ such that $r' \leq r/\log r$. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
circuit complexity / monotone circuit / lower bound / merging function / majority function / / / |
| Reference Info. |
IEICE Tech. Rep., vol. 106, no. 128, COMP2006-19, pp. 15-19, June 2006. |
| Paper # |
COMP2006-19 |
| Date of Issue |
2006-06-16 (COMP) |
| ISSN |
Print edition: ISSN 0913-5685 |
| Download PDF |
|
| Conference Information |
| Committee |
COMP |
| Conference Date |
2006-06-23 - 2006-06-23 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Saitama Univ. |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
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| Paper Information |
| Registration To |
COMP |
| Conference Code |
2006-06-COMP |
| Language |
English |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
Reductions for Monotone Boolean Circuits |
| Sub Title (in English) |
|
| Keyword(1) |
circuit complexity |
| Keyword(2) |
monotone circuit |
| Keyword(3) |
lower bound |
| Keyword(4) |
merging function |
| Keyword(5) |
majority function |
| Keyword(6) |
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| Keyword(7) |
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| Keyword(8) |
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| 1st Author's Name |
Kazuo Iwama |
| 1st Author's Affiliation |
Kyoto University (Kyoto Univ.) |
| 2nd Author's Name |
Hiroki Morizumi |
| 2nd Author's Affiliation |
Kyoto University (Kyoto Univ.) |
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| Speaker |
Author-2 |
| Date Time |
2006-06-23 11:10:00 |
| Presentation Time |
35 minutes |
| Registration for |
COMP |
| Paper # |
COMP2006-19 |
| Volume (vol) |
vol.106 |
| Number (no) |
no.128 |
| Page |
pp.15-19 |
| #Pages |
5 |
| Date of Issue |
2006-06-16 (COMP) |