Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR19-139 | 8th October 2019 21:26

Direct sum testing - the general case

RSS-Feed




TR19-139
Authors: Irit Dinur, Konstantin Golubev
Publication: 8th October 2019 21:27
Downloads: 112
Keywords: 


Abstract:


A function f:[n_1] x ... x [n_d]-->F is a direct sum if it is of the form f(a_1,...,a_d) = f_1(a_1) + ... + f_d (a_d) (mod 2) for some d functions f_i:[n_i]-->F_i for all i=1,...,d. 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 an agreement test which slightly generalizes the direct product test.

In multiplicative {+1,-1} notation, our result reads as follows. A d-dimensional tensor with {+1,-1} entries is called a tensor product if it is a tensor product of d vectors with {+1,-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.

We also present a different test, which queries the function at most (d+2) times, but is easier to analyze.



ISSN 1433-8092 | Imprint