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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.

具有多个收发器的系统中的数据通信提出了由复杂数据相关模式、网络拓扑和交互场景的可能性引起的难题。传统上，这些问题是使用信息理论（IT）的工具来解决的，它假设数据是根据某种生成模型产生的。在实践中，大多数时候生成模型是未知的。即使它是已知的，它往往比通常用于理论研究的模型更复杂。这个项目将使用来自计算机信息理论（AIT，也称为Kolmogorov复杂性）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。其优点是，新方法不依赖于任何模型，因此，这种方式获得的结果是有效的，在更一般的情况下。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和活跃的思想交流。该项目将产生新的见解Kolmogorov复杂性和通信复杂性。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。这些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应用前景的研究活动。该项目是及时和现实的，因为最近已经变得明显，一些有趣的问题（例如，非遍历信源的信源编码），这不能用基于香农熵的工具来处理，可以在AIT框架中解决。在另一个方向上，最近在Kolmogorov复杂性的一些经典问题上取得了进展，这些问题受到IT结果和技术的启发。该项目将：（1）分离、理解和发展Kolmogorov复杂性的某些方面，这些方面与数据通信特别相关;（2）利用新开发的工具，在信道编码、网络编码、交互协议等网络通信中的突出问题上取得进展，及其他;以及（3）使用来自通信环境的见解来推进Kolmogorov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知识价值和更广泛的影响审查标准进行评估而被认为值得支持。

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