Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions. We build upon and make explicit earlier implicit results of Viola to provide superconstant lower bounds on the locality of Boolean functions approximately sampling the uniform distribution over binary strings of particular Hamming weights, both exactly and modulo an integer, answering questions of Viola (Journal of Computing 2012) and Filmus, Leigh, Riazanov, and Sokolov (RANDOM 2023). Applications to data structure lower bounds and quantum-classical separations are discussed.

翻译：受Viola（Journal of Computing 2012）开创性工作的推动，过去十年间，研究界对（近似）采样分布复杂性的探索日趋活跃，这与传统侧重函数计算复杂性的研究形成鲜明对比。我们依托并明确阐释了Viola此前隐含的结果，针对精确模整数与模整数两种情形，为近似采样特定汉明权重二进制串均匀分布的布尔函数，提供了超常数下界——既涵盖精确采样情形，也涵盖取模情形，从而回答了Viola（Journal of Computing 2012）及Filmus、Leigh、Riazanov与Sokolov（RANDOM 2023）提出的问题。此外，本文还讨论了相关结论在数据结构下界及量子-经典区分性方面的应用。