# Editing Open Problems:66

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Acharya, Canonne, and Kamath {{cite|AcharyaCK-14}} showed that $\Omega(\sqrt{\log \log n})$ conditional queries are needed in this case for some constant $\epsilon > 0$. Contrary to the case of only one distribution unknown, if both distributions are unknown, the required number of queries is a function of $n$. Falahatgar, Jafarpour, Orlitsky, Pichapathi, and Suresh {{cite|FalahatgarJOPS-15}} showed that $O\left(\frac{\log{\log{n}}}{\epsilon^5}\right)$ queries are sufficient. This determines the query complexity of the problem up to a factor of $\sqrt{\log \log n}$. | Acharya, Canonne, and Kamath {{cite|AcharyaCK-14}} showed that $\Omega(\sqrt{\log \log n})$ conditional queries are needed in this case for some constant $\epsilon > 0$. Contrary to the case of only one distribution unknown, if both distributions are unknown, the required number of queries is a function of $n$. Falahatgar, Jafarpour, Orlitsky, Pichapathi, and Suresh {{cite|FalahatgarJOPS-15}} showed that $O\left(\frac{\log{\log{n}}}{\epsilon^5}\right)$ queries are sufficient. This determines the query complexity of the problem up to a factor of $\sqrt{\log \log n}$. | ||

β | In the non-adaptive model, Kamath and Tzamos {{cite|KamathT-19}} showed that $\ | + | In the non-adaptive model, Kamath and Tzamos {{cite|KamathT-19}} showed that $\poly \log n$ conditional queries are sufficient for equivalence testing. A lower bound of $\Omega(\log n)$ by Acharya, Canonne, and Kamath {{cite|AcharyaCK-14}} for uniformity testing shows that identity and equivalence testing have complexities related by polynomial factors in the non-adaptive model, compared to the gap in the adaptive model. |