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Direct Product Testing

2014 IEEE 29th Conference on Computational Complexity (CCC), 2014
A direct product function is a function of the form g(x_1, ldots, x_k)=(g_1(x_1), ldots, g_k(x_k)). We show that the direct product property is locally testable with two queries, that is, a canonical two-query test distinguishes between direct product functions and functions that are far from direct products with constant probability.
Irit Dinur, David Steurer
openaire   +2 more sources

A direct product theorem for quantum communication complexity with applications to device-independent QKD

IEEE Annual Symposium on Foundations of Computer Science, 2022
We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product distributions.
Rahul Jain, Srijita Kundu
semanticscholar   +1 more source

Direct product in BG-algebras

International Journal of Algebra, 2019
In this paper, we introduce the notion of direct product in BG-algebras and some related properties. Also, we introduce the notion about BG-homomorphism of direct product in BG-algebras and we obtain some of its properties.
S. Widianto   +3 more
semanticscholar   +1 more source

Hypercubes As Direct Products

SIAM Journal on Discrete Mathematics, 2005
Summary: Let \(G\) be a connected bipartite graph. An involution \(\alpha\) of \(G\) that preserves the bipartition of \(G\) is called bipartite. Let \(G^\alpha\) be the graph obtained from \(G\) by adding to \(G\) the natural perfect matching induced by \(\alpha\). We show that the \(k\)-cube \(Q_{k}\) is isomorphic to the direct product \(G \times H\)
Brešar, Boštjan   +3 more
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