The Corruption Bound, Log Rank, and Communication Complexity
Adi Shraibman
TL;DR
This paper establishes upper bounds on deterministic communication complexity using rank and corruption bounds, simplifying previous results and providing elementary proofs for known bounds.
Contribution
It offers simplified proofs and bounds relating communication complexity to rank and corruption bounds, building on prior work by Gavinsky, Lovett, and others.
Findings
Upper bounds on deterministic communication complexity in terms of log rank.
Simplified proofs of existing bounds using elementary methods.
Connections between corruption bounds and communication complexity.
Abstract
We prove upper bounds on deterministic communication complexity in terms of log of the rank and simple versions of the corruption bound. Our bounds are a simplified version of the results of Gavinsky and Lovett, using the same set of tools. We also give an elementary proof for the upper bound on communication complexity in terms of rank proved by Lovett.
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