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AF: Small: RUI: New Directions in Kolmogorov Complexity and Network Information Theory

AF：小：RUI：柯尔莫哥洛夫复杂性和网络信息理论的新方向

基本信息

批准号：
1811729
负责人：
Marius Zimand
金额：
$ 23.62万
依托单位：
Towson University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-10-01 至 2022-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811729&HistoricalAwards=false
关键词：
AF Small RUI New Directions

项目摘要

Data communication in systems with multiple senders and receivers raises difficult problems caused by the possibility of complex data correlation patterns, network topologies, and interaction scenarios. Traditionally, these problems have been tackled using tools from Information Theory (IT), which assumes that the data has been produced according to a certain generative model. In practice, most of the time the generative model is not known. Even if it is known, it is often more complicated than the models typically used in theoretical studies. This project will use tools from Algorithmic Information Theory (AIT, also known as Kolmogorov complexity), which equates the information in a piece of data with its minimal description length. The advantage is that the new approach does not rely on any model, and consequently the results obtained this way are valid in more general circumstances. The problems that will be studied are of interest to computer scientists, electrical engineers, and mathematicians. The project will promote a deep and dynamic exchange of ideas between these communities. This project will produce new insights in Kolmogorov complexity and communication complexity. These areas have applications in computational complexity, machine learning, constructive combinatorics, and other fields. The results will likely have an impact in many of these areas. The project will allow undergraduate and graduate students to participate in research activities that have a strong theoretical flavor and the promise of real-world applications.The project is timely and realistic because it has recently become apparent that some interesting questions (for instance, source coding of non-ergodic sources), which cannot be approached with tools based on Shannon entropy, can be solved in the AIT framework. In the other direction, there has been recent progress in some classical problems in Kolmogorov complexity inspired from results and techniques from IT. The project will: (1) isolate, understand, and develop certain aspects of Kolmogorov complexity that are particularly relevant for data communication; (2) use the newly-developed tools to make progress in outstanding problems in network communication such as channel coding, network coding, interactive protocols, and others; and (3) use the insights from the communication setting to advance the theory of Kolmogorov complexity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

具有多个发送器和接收器的系统中的数据通信由于复杂的数据关联模式、网络拓扑和交互场景的可能性而引起了难题。传统上，这些问题是使用信息论 (IT) 的工具来解决的，信息论假设数据是根据某种生成模型生成的。在实践中，大多数时候生成模型是未知的。即使它是已知的，它通常也比理论研究中通常使用的模型更复杂。该项目将使用算法信息论（AIT，也称为柯尔莫哥洛夫复杂度）的工具，它将一段数据中的信息与其最小描述长度等同起来。优点是新方法不依赖于任何模型，因此这种方法获得的结果在更一般的情况下是有效的。将要研究的问题是计算机科学家、电气工程师和数学家感兴趣的。该项目将促进这些社区之间深入、动态的思想交流。该项目将对柯尔莫哥洛夫复杂性和通信复杂性产生新的见解。这些领域在计算复杂性、机器学习、构造组合学和其他领域都有应用。结果可能会对其中许多领域产生影响。该项目将允许本科生和研究生参与具有浓厚理论色彩和现实世界应用前景的研究活动。该项目是及时且现实的，因为最近已经发现一些有趣的问题（例如，非遍历源的源代码编码）无法使用基于香农熵的工具来解决，但可以在 AIT 框架中解决。另一方面，受 IT 结果和技术的启发，柯尔莫哥洛夫复杂性的一些经典问题最近取得了进展。该项目将：（1）分离、理解和开发与数据通信特别相关的柯尔莫哥洛夫复杂性的某些方面；（二）利用新开发的工具，攻克信道编码、网络编码、交互协议等网络通信中的突出问题； (3) 利用通信环境中的见解来推进柯尔莫哥洛夫复杂性理论。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（4）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Secret Key Agreement from Correlated Data, with No Prior Information

相关数据的密钥协议，无需先验信息

DOI：
10.4230/lipics.stacs.2020.21
发表时间：
2020
期刊：
37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020
影响因子：
0
作者：
Zimand, Marius
通讯作者：
Zimand, Marius

Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity

时限柯尔莫哥洛夫复杂度中的最优编码定理