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| Presentation | 2008-12-03 14:35 Improved Formula Size Lower Bounds for Monotone Self-Dual Boolean Functions Kenya Ueno (Univ. of Tokyo)  COMP2008-51 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan~\cite{KKN95} and the theory of stable set polytope. We apply it to majority functions and prove their formula size lower bounds improved from the classical result by Khrapchenko~\cite{Khrapchenko71}. Moreover, we introduce a notion of unbalanced recursive ternary majority functions motivated by a decomposition theory of monotone self-dual functions and give integrally matching upper and lower bounds of their formula size. We also show monotone formula size lower bounds of balanced recursive ternary majority functions improved from the quantum adversary bound of Laplante, Lee and Szegedy~\cite{LLS06}. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Formula Size Lower Bounds / Linear Programming / Clique Constraints / Majority Function / Communication Complexity / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 108, no. 330, COMP2008-51, pp. 33-40, Dec. 2008. | |
| Paper # | COMP2008-51 | |
| Date of Issue | 2008-11-26 (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 | COMP2008-51 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2008-12-03 - 2008-12-03 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Gunma Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2008-12-COMP |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Improved Formula Size Lower Bounds for Monotone Self-Dual Boolean Functions |
| Sub Title (in English) | |
| Keyword(1) | Formula Size Lower Bounds |
| Keyword(2) | Linear Programming |
| Keyword(3) | Clique Constraints |
| Keyword(4) | Majority Function |
| Keyword(5) | Communication Complexity |
| Keyword(6) | |
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| Keyword(8) | |
| 1st Author's Name | Kenya Ueno |
| 1st Author's Affiliation | The University of Tokyo (Univ. of Tokyo) |
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| Speaker | Author-1 |
| Date Time | 2008-12-03 14:35:00 |
| Presentation Time | 35 minutes |
| Registration for | COMP |
| Paper # | COMP2008-51 |
| Volume (vol) | vol.108 |
| Number (no) | no.330 |
| Page | pp.33-40 |
| #Pages | 8 |
| Date of Issue | 2008-11-26 (COMP) |
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