从子立方体划分复杂性中分离决策树复杂性
Separating decision tree complexity from subcube partition complexity
摘要：
计算的子立方体划分模型至少与决策树一样强大，但这些模型之间没有分离。我们证明了存在一个函数，其确定性子立方体划分复杂度渐近小于其随机决策树复杂度，解决了Friedgut，Kahn和Wigderson（2002）的一个公开问题。我们的下界是基于信息理论的技术，首先介绍了下界的随机决策树复杂性的递归多数函数。我们还表明，公共硬币分区界，最有名的下界方法随机决策树复杂性，包括其他一般技术，如块敏感性，近似度，随机证书的复杂性，和经典的对手界，也下界随机子立方体分区复杂性。这表明所有这些下界技术都不能证明随机决策树复杂度的最优下界，这回答了Jain和Klauck（2010）以及Jain，Lee和Vishnoi（2014）的一个开放问题。
英文摘要：
The subcube partition model of computation is at least as powerful as decision trees but no separation between these models was known. We show that there exists a function whose deterministic subcube partition complexity is asymptotically smaller than its randomized decision tree complexity, resolving an open problem of Friedgut, Kahn, and Wigderson (2002). Our lower bound is based on the information-theoretic techniques first introduced to lower bound the randomized decision tree complexity of the recursive majority function. We also show that the public-coin partition bound, the best known lower bound method for randomized decision tree complexity subsuming other general techniques such as block sensitivity, approximate degree, randomized certificate complexity, and the classical adversary bound, also lower bounds randomized subcube partition complexity. This shows that all these lower bound techniques cannot prove optimal lower bounds for randomized decision tree complexity, which answers an open question of Jain and Klauck (2010) and Jain, Lee, and Vishnoi (2014).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
