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what is the largest gap between rank and approximate rank?

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  • What is the largest gap between rank and approximate rank?

    We know that the log of the rank of a 0-1 matrix is the lower bound of deterministic communication complexity, and the log of the approximate rank is the lower bound of randomized communication complexity. The largest gap between deterministic communication complexity and randomized communication complexity is exponential. So what about the gap between rank and approximate rank of a boolean matrix?

    Answer:

    First I'll give some background and define approximate rank. A good reference is the recent survey by...

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