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 |
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) |
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COMP2013-11 |
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 |
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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) |
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witness finding |
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blackbox reduction |
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query complexity |
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lower bound |
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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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Speaker |
Author-3 |
Date Time |
2013-05-17 13:35:00 |
Presentation Time |
25 minutes |
Registration for |
COMP |
Paper # |
COMP2013-11 |
Volume (vol) |
vol.113 |
Number (no) |
no.50 |
Page |
pp.39-46 |
#Pages |
8 |
Date of Issue |
2013-05-10 (COMP) |
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