使用Oracle的实例复杂性度量通信复杂性
Measuring communication complexity using instance complexity with oracles
摘要：
我们建立了非确定性通信复杂性和实例复杂性之间的联系，这是一种基于算法熵的信息度量。令$\overline{x}$、$\overline{y}$和$Y_1(\overline{x})$分别为Alice已知的输入、Bob已知的输入以及$y$的所有值的集合，使得$f(\overline{x},y)=1$ ;字符串是非确定性通信协议的见证，当且仅当它是程序$p$，其“精确地对应”于实例复杂度$\ic^{f,t}(\overline{y}:Y_1(\overline{x}))$。
英文摘要：
We establish a connection between non-deterministic communication complexity and instance complexity, a measure of information based on algorithmic entropy. Let $\overline{x}$, $\overline{y}$ and $Y_1(\overline{x})$ be respectively the input known by Alice, the input known by Bob, and the set of all values of $y$ such that $f(\overline{x},y)=1$; a string is a witness of the non-deterministic communication protocol iff it is a program $p$ that "corresponds exactly" to the instance complexity $\ic^{f,t}(\overline{y}:Y_1(\overline{x}))$.
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。
