AI 中文总结
该研究针对带符号子立方体表示，获得近似广义权重与稀疏度的指数上界，建立对偶下界框架，推导其与量子查询复杂度的帕图里型关联，完善相关理论刻画。
AI 中文摘要
我们基于最深转换深度D(F)，得到近似广义权重和近似广义稀疏度的指数上界，并证明这些上界在指数因子的常数倍范围内是最优的。我们进一步刻画近似广义稀疏度，建立基于指数限制轮廓的对偶下界框架，并推导将近似广义权重与量子查询复杂度关联起来的帕图里型刻画。
英文摘要
We obtain exponential upper bounds on approximate generalized weight and generalized sparsity in terms of the deepest transition depth D(F), and show that these bounds are optimal up to constant factors in the exponent. We further characterize approximate generalized sparsity, establish a dual lower-bound framework based on exponential restriction profiles, and derive a Paturi-type characterization relating approximate generalized weight to quantum query complexity.
Comments20 pages
