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Paper Abstract and Keywords
Presentation 2013-05-17 13:35
Query Complexity of Witness Finding
Akinori Kawachi (Tokyo Inst. of Tech.), Benjamin Rossman (NII), Osamu Watanabe (Tokyo Inst. of Tech.) COMP2013-11
Abstract (in Japanese) (See Japanese page) 
(in English) For any polynomial-time relation L subset_of {0,1}^m x {0,1}^n where n = m^{O(1)}, the classic search-to-decision reduction of Ben-David, Chor, Goldreich and Luby gives a BPP_||^NP algorithm which solves the search problem for L (given x, find w such that (x,w) in L) with only O(n^2) non-adaptive queries to the NP oracle. We begin by observing that this algorithm is black-box in the following sense: it can be implemented in the setting where the input x is unavailable and, instead, only the witness set {w : (x,w) in L} is provided as a black-box. Our main result is a tight lower bound in this black-box setting: we show that every such black-box BPP_||^NP search-to-decision reduction requires Omega(n^2) non-adaptive queries to the NP oracle. As the framework for proving this lower bound, we introduce a general witness finding problem with respect to a class W of witness sets and a class Q of queries. In addition to NP-type queries, we prove lower bounds for monotone queries as well as for affine witness sets.
Keyword (in Japanese) (See Japanese page) 
(in English) witness finding / blackbox reduction / query complexity / lower bound / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 50, COMP2013-11, pp. 39-46, May 2013.
Paper # COMP2013-11 
Date of Issue 2013-05-10 (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 IPSJ-AL  
Conference Date 2013-05-17 - 2013-05-18 
Place (in Japanese) (See Japanese page) 
Place (in English) Otaru University of Commerce 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2013-05-COMP-AL 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Query Complexity of Witness Finding 
Sub Title (in English)  
Keyword(1) witness finding  
Keyword(2) blackbox reduction  
Keyword(3) query complexity  
Keyword(4) lower bound  
1st Author's Name Akinori Kawachi  
1st Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech.)
2nd Author's Name Benjamin Rossman  
2nd Author's Affiliation National Institute of Informatics (NII)
3rd Author's Name Osamu Watanabe  
3rd Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech.)
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Date Time 2013-05-17 13:35:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2013-11 
Volume (vol) IEICE-113 
Number (no) no.50 
Page pp.39-46 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2013-05-10 

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