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Paper Abstract and Keywords
Presentation 2010-12-03 10:30
Hard Functions for Low-degree Polynomials over Prime Fields (Extended Abstract)
Andrej Bogdanov (Chinese Univ. of Hong Kong), Akinori Kawachi, Hidetoki Tanaka (Tokyo Inst. of Tech.) COMP2010-39
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we present a new hardness amplification for low-degree polynomials over prime fields, namely, we prove that if some function is mildly hard to approximate by any low-degree polynomials then the sum of independent copies of the function is very hard to approximate by them. This result generalizes the XOR lemma for low-degree polynomials over the binary field given by Viola and Wigderson. The main technical contribution is the analysis of the Gowers norm over prime fields. For the analysis, we discuss a generalized low-degree test, which we call the Gowers test, for polynomials over prime fields, which is a natural generalization of that over the binary field given by Alon, Kaufman, Krivelevich, Litsyn and Ron. This Gowers test provides a new technique to analyze the Gowers norm over prime fields. By using our argument, we also prove the hardness of modulo functions for low-degree polynomials over prime fields. This article is a technical report without peer-review, and the full version will be published elsewhere.
Keyword (in Japanese) (See Japanese page) 
(in English) low-degree polynomial / hardness amplification / Gowers norm / / / / /  
Reference Info. IEICE Tech. Rep., vol. 110, no. 325, COMP2010-39, pp. 1-6, Dec. 2010.
Paper # COMP2010-39 
Date of Issue 2010-11-26 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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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Conference Information
Committee COMP  
Conference Date 2010-12-03 - 2010-12-03 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyutech Plaza, Kyushu Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2010-12-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Hard Functions for Low-degree Polynomials over Prime Fields (Extended Abstract) 
Sub Title (in English)  
Keyword(1) low-degree polynomial  
Keyword(2) hardness amplification  
Keyword(3) Gowers norm  
1st Author's Name Andrej Bogdanov  
1st Author's Affiliation the Chinese University of Hong Kong (Chinese Univ. of Hong Kong)
2nd Author's Name Akinori Kawachi  
2nd Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech.)
3rd Author's Name Hidetoki Tanaka  
3rd Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech.)
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Date Time 2010-12-03 10:30:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2010-39 
Volume (vol) IEICE-110 
Number (no) no.325 
Page pp.1-6 
#Pages IEICE-6 
Date of Issue IEICE-COMP-2010-11-26 

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