arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1106.3595cs.ITcs.CCmath.IT
收藏

信息等于分期付款的通信

Information Equals Amortized Communication

Mark Braverman, Anup Rao

摘要:

我们展示了如何有效地模拟发送的消息M的接收器谁有部分信息的消息,使预期的比特数在模拟中沟通的是接近的额外的信息量的消息透露给接收器。这是Slepian-Wolf定理的推广和加强,该定理显示了在M是X的确定性函数的情况下如何以低摊销通信进行这样的模拟。一个警告是,我们的模拟是交互式的。因此,我们证明了内部信息成本(即信息透露给各方)参与计算任何关系或功能使用两方交互式协议是完全等于摊销通信复杂性计算独立的副本相同的关系或功能。我们还表明,唯一的方法来证明一个强直和定理随机通信复杂性是通过解决一个特定的变量,我们定义的指针跳跃问题。我们的工作意味着一个强直和定理的通信复杂性保持当且仅当有效的压缩通信协议是可能的。

英文摘要:

We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver. This is a generalization and strengthening of the Slepian-Wolf theorem, which shows how to carry out such a simulation with low amortized communication in the case that M is a deterministic function of X. A caveat is that our simulation is interactive. As a consequence, we prove that the internal information cost (namely the information revealed to the parties) involved in computing any relation or function using a two party interactive protocol is exactly equal to the amortized communication complexity of computing independent copies of the same relation or function. We also show that the only way to prove a strong direct sum theorem for randomized communication complexity is by solving a particular variant of the pointer jumping problem that we define. Our work implies that a strong direct sum theorem for communication complexity holds if and only if efficient compression of communication protocols is possible.

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。

↑