陪集决策树与傅里叶代数
Coset decision trees and the Fourier algebra
University of Oxford（牛津大学）
AI总结：
本文证明有限群上傅里叶代数范数有界的{0,1}值函数可由叶子数呈三重指数增长的陪集决策树计算，并给出逆方向指数上界。
摘要：
我们证明，若G是有限群且f是G上取值于{0,1}且傅里叶代数范数至多为M的函数，则f可由至多exp(exp(exp(O(M^2))))个叶子的陪集决策树（即在每个顶点查询给定陪集成员资格的决策树）计算。简短计算表明，任何可由具有m个叶子的陪集决策树计算的{0,1}值函数的傅里叶代数范数至多为exp(O(m))。
英文摘要：
We show that if G is a finite group and f is a {0,1}-valued function on G with Fourier algebra norm at most M then f may be computed by a coset decision tree (that is a decision tree in which at each vertex we query membership of a given coset) having at most \exp(\exp(\exp(O(M^2)))) leaves. A short calculation shows that any {0,1}-valued function which may be computed by a coset decision tree with m leaves has Fourier algebra norm at most \exp(O(m)).
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。
