We prove an \Omega(n/k+k) communication lower bound on (k-1)-round distributional complexity of the k-step pointer chasing problem under uniform input distribution, improving the \Omega(n/k - k log n) lower bound due to Yehudayoff (Combinatorics Probability and Computing, 2020). Our lower bound almost matches the upper bound of O(n/k + k) communication by Nisan and Wigderson (STOC 91). As part of our approach, we put forth gadgetless lifting, a new framework that lifts lower bounds for a family of restricted protocols into lower bounds for general protocols. A key step in gadgetless lifting is choosing the appropriate definition of restricted protocols. In this paper, our definition of restricted protocols is inspired by the structure-vs-pseudorandomness decomposition by G\"o\"os, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24). Previously, round-communication trade-offs were mainly obtained by round elimination and information complexity. Both methods have some barriers in some situations, and we believe gadgetless lifting could potentially address these barriers.

翻译：我们证明了在均匀输入分布下，k步指针追逐问题的(k-1)轮分布复杂度具有Ω(n/k+k)的通信下界，改进了Yehudayoff（《组合学、概率与计算》，2020年）提出的Ω(n/k - k log n)下界。我们的下界几乎匹配了Nisan和Wigderson（STOC 91）提出的O(n/k + k)通信上界。作为方法的一部分，我们提出了无小工具提升这一新框架，该框架能将受限协议族的下界提升为一般协议的下界。无小工具提升的关键步骤是选择合适的受限协议定义。本文中，我们对受限协议的定义受到Göös、Pitassi和Watson（FOCS 17）以及Yang和Zhang（STOC 24）提出的结构-伪随机性分解的启发。此前，轮次-通信权衡主要通过轮次消除和信息复杂度方法获得。这两种方法在某些情况下存在局限性，我们相信无小工具提升有望突破这些局限。