Editing Open Problems:77
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β | In the $\mathbf{UPP}$ communication model, two parties execute a (private coin) randomized communication protocol, and must output the correct answer with probability strictly greater than 1/2. Forster {{cite|Forster-01}} proved a linear lower bound on the $\mathbf{UPP}$ communication complexity of Inner Product Mod 2. $\mathbf{UPP}$ is essentially the most powerful two-party communication model against which we know how to prove lower bounds.<ref>Let us ignore the example of | + | In the $\mathbf{UPP}$ communication model, two parties execute a (private coin) randomized communication protocol, and must output the correct answer with probability strictly greater than 1/2. Forster {{cite|Forster-01}} proved a linear lower bound on the $\mathbf{UPP}$ communication complexity of Inner Product Mod 2. $\mathbf{UPP}$ is essentially the most powerful two-party communication model against which we know how to prove lower bounds.<ref> Let us ignore the example of Parity-P, which can compute Inner Product Mod 2 with constant communication, yet a linear lower bound on the Parity-P communication complexity of Equality follows from a matrix rank argument.</ref> |
The (informal) open question is to prove a superlogarithmic lower bound for any natural communication complexity class that can compute problems outside of $\mathbf{UPP}$. | The (informal) open question is to prove a superlogarithmic lower bound for any natural communication complexity class that can compute problems outside of $\mathbf{UPP}$. |