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Electronic Colloquium on Computational Complexity

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Reports tagged with dimension complexity:
TR19-027 | 1st March 2019
Mark Bun, Nikhil Mande, Justin Thaler

Sign-Rank Can Increase Under Intersection

The communication class $UPP^{cc}$ is a communication analog of the Turing Machine complexity class $PP$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension complexity), and is essentially the most powerful communication class against which we know how to prove lower bounds.

For a communication problem ... more >>>

TR22-130 | 15th September 2022
Hamed Hatami, Kaave Hosseini, Xiang Meng

A Borsuk-Ulam lower bound for sign-rank and its application

We introduce a new topological argument based on the Borsuk-Ulam theorem to prove a lower bound on sign-rank.

This result implies the strongest possible separation between randomized and unbounded-error communication complexity. More precisely, we show that for a particular range of parameters, the randomized communication complexity of ... more >>>

ISSN 1433-8092 | Imprint