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arXiv · 1307.3543

A Short Proof that the Extension Complexity of the Correlation Polytope Grows Exponentially

Volker Kaibel·Stefan Weltge
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Abstract

We establish that the extension complexity of the nXn correlation polytope is at least 1.5^n by a short proof that is self-contained except for using the fact that every face of a polyhedron is the intersection of all facets it is contained in. The main innovative aspect of the proof is a simple combinatorial argument showing that the rectangle covering number of the unique-disjointness matrix is at least 1.5^n, and thus the nondeterministic communication complexity of the unique-disjointness predicate is at least .58n. We thereby slightly improve on the previously best known lower bounds 1.24^n and .31n, respectively.

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Volker Kaibel, Stefan Weltge. 2016-02-25. A Short Proof that the Extension Complexity of the Correlation Polytope Grows Exponentially. https://doi.org/10.1007/s00454-014-9655-9

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