Direct sum testing: The general case

Irit Dinur, Konstantin Golubev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A function f : [n1] × · · · × [nd] → F2 is a direct sum if it is of the form f (a1,..., ad) = f1(a1) ⊕ ... ⊕ fd(ad), for some d functions fi : [ni] → F2 for all i = 1, ..., d, and where n1, ..., nd ∊ N. We present a 4-query test which distinguishes between direct sums and functions that are far from them. The test relies on the BLR linearity test (Blum, Luby, Rubinfeld, 1993) and on the direct product test constructed by Dinur & Steurer (2014). We also present a different test, which queries the function (d + 1) times, but is easier to analyze. In multiplicative ±1 notation, this reads as follows. A d-dimensional tensor with ±1 entries is called a tensor product if it is a tensor product of d vectors with ±1 entries, or equivalently, if it is of rank 1. The presented tests can be read as tests for distinguishing between tensor products and tensors that are far from being tensor products.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
EditorsDimitris Achlioptas, Laszlo A. Vegh
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771252
DOIs
StatePublished - Sep 2019
Event22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 - Cambridge, United States
Duration: 20 Sep 201922 Sep 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume145
ISSN (Print)1868-8969

Conference

Conference22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Country/TerritoryUnited States
CityCambridge
Period20/09/1922/09/19

All Science Journal Classification (ASJC) codes

  • Software

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