In interactive coding, Alice and Bob wish to compute some function $f$ of their individual private inputs $x$ and $y$. They do this by engaging in an interactive protocol to jointly compute $f(x,y)$. The goal is to do this in an error-resilient way, such that even given some fraction of adversarial corruptions to the protocol, both parties still learn $f(x,y)$. Typically, the error resilient protocols constructed by interactive coding schemes are \emph{non-adaptive}, that is, the length of the protocol as well as the speaker in each round is fixed beforehand. The maximal error resilience obtainable by non-adaptive schemes is now well understood. In order to circumvent known barriers and achieve higher error resilience, the work of Agrawal, Gelles, and Sahai (ISIT 2016) introduced to interactive coding the notion of \emph{adaptive} schemes, where the length of the protocol or the speaker order are no longer necessarily fixed. In this paper, we study the power of \emph{adaptive termination} in the context of the error resilience of interactive coding schemes. In other words, what is the power of schemes where Alice and Bob are allowed to disengage from the protocol early? We study this question in two contexts, both for the task of \emph{message exchange}, where the goal is to learn the other party's input.

翻译：在交互式编码中，Alice和Bob希望根据各自的私有输入x和y计算某个函数f。他们通过执行交互协议来共同计算f(x,y)。目标是以具有错误弹性的方式实现这一过程，使得即使在协议遭受一定比例的恶意破坏时，双方仍能获知f(x,y)。通常，由交互式编码方案构造的错误弹性协议是“非自适应”的，即协议的长度以及每一轮的发言者事先固定。非自适应方案所能达到的最大错误弹性现在已得到充分理解。为了突破已知障碍并实现更高的错误弹性，Agrawal、Gelles和Sahai（ISIT 2016）的工作引入了交互式编码中“自适应”方案的概念，其中协议的长度或发言顺序不再必然固定。在本文中，我们研究“自适应终止”在交互式编码方案错误弹性方面的能力。换言之，允许Alice和Bob提前退出协议时，方案能带来何种优势？我们在两个背景下研究这一问题，均针对“消息交换”任务，即目标是获知对方的输入。