We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove new bounds on the number of relevant variables for boolean functions in terms of a variety of complexity measures. Our approach unifies and refines all previously known bounds of this type. We also improve Nisan and Szegedy's well-known block sensitivity vs. degree inequality by a constant factor, thereby improving Huang's recent proof of the sensitivity conjecture by the same constant.

翻译：我们在最近一篇关于Chiarelli、Hatami和Saks的论文中概括和扩展了这些想法,以从各种复杂措施的角度来证明关于布林功能相关变量数量的新界限。我们的方法统一和完善了所有以前已知的这种类型的界限。我们还用一个不变的因素来提高尼桑和泽格迪众所周知的区块敏感性和程度不平等,从而改进黄蜂最近关于同一常数敏感度推测的证据。