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DOI: 10.4230/LIPIcs.FSTTCS.2017.10
URN: urn:nbn:de:0030-drops-83967
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8396/
Anshu, Anurag ; Gavinsky, Dmitry ; Jain, Rahul ; Kundu, Srijita ; Lee, Troy ; Mukhopadhyay, Priyanka ; Santha, Miklos ; Sanyal, Swagato
A Composition Theorem for Randomized Query Complexity
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Abstract
Let the randomized query complexity of a relation for error probability epsilon be denoted by R_epsilon(). We prove that for any relation f contained in {0,1}^n times R and Boolean function g:{0,1}^m -> {0,1}, R_{1/3}(f o g^n) = Omega(R_{4/9}(f).R_{1/2-1/n^4}(g)), where f o g^n is the relation obtained by composing f and g. We also show using an XOR lemma that R_{1/3}(f o (g^{xor}_{O(log n)})^n) = Omega(log n . R_{4/9}(f) . R_{1/3}(g))$, where g^{xor}_{O(log n)} is the function obtained by composing the XOR function on O(log n) bits and g.
BibTeX - Entry
@InProceedings{anshu_et_al:LIPIcs:2018:8396,
author = {Anurag Anshu and Dmitry Gavinsky and Rahul Jain and Srijita Kundu and Troy Lee and Priyanka Mukhopadhyay and Miklos Santha and Swagato Sanyal},
title = {{A Composition Theorem for Randomized Query Complexity}},
booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
pages = {10:1--10:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-055-2},
ISSN = {1868-8969},
year = {2018},
volume = {93},
editor = {Satya Lokam and R. Ramanujam},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8396},
URN = {urn:nbn:de:0030-drops-83967},
doi = {10.4230/LIPIcs.FSTTCS.2017.10},
annote = {Keywords: Query algorithms and complexity, Decision trees, Composition theorem, XOR lemma, Hardness amplification}
}
| Keywords: | Query algorithms and complexity, Decision trees, Composition theorem, XOR lemma, Hardness amplification | |
| Seminar: | 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017) | |
| Issue date: | 2018 | |
| Date of publication: | 12.02.2018 |
