Before revision:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, improving upon both the known upper and lower bounds in [CRS15].
After revision:  \tilde{O})-query algorithm for monotonicity testing in the conditional sampling model, improving on the }\tilde{O} ] Finally, we study (non-tolerant) identity testing under the pair conditional sampling model, and provide a tight bound of \tilde{\Theta}( \sqrt{\log n \cdot \varepsilon^{-2}) for the query complexity, where the domain of the distribution has size N. This improves upon both the known upper and lower bounds in [CRS15].