题目：Proving Information Inequalities and Identities with Symbolic Computation

摘要：Proving linear inequalities and identities of Shannon's information measures, possibly with linear constraints on the information measures, is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and implemented, which are all based on solving a linear program (LP). In particular, an identity $f = 0$ is verified by solving two LPs, one for $f \ge 0$ and one for $f \le 0$.

In this paper, we develop a set of algorithms that can be implemented by symbolic computation. Based on these algorithms, procedures for verifying linear information inequalities and identities are devised. Compared with LP-based algorithms, our procedures can produce analytical proofs that are both human-verifiable and free of numerical errors. Our procedures are also more efficient computationally. For constrained inequalities, by taking advantage of the algebraic structure of the problem, the size of the LP that needs to be solved can be significantly reduced. For identities, instead of solving two LPs, the identity can be verified directly with very little computation.

This is a joint work with Raymond W. Yeung and Xiao-Shan Gao.

报告人简介：（郭来刚）Laigang Guo received the Ph.D. degree in applied mathematics from University of Chinese Academy of Sciences, Beijing, China, in 2019. He joined NCMIS, Academy of Mathematics and Systems Science and INC, The Chinese University of Hong Kong as a postdoctoral fellow in 2019 and 2021 respectively. Currently, he is an assistant professor with SMS, Beijing Normal University. His research interests are symbolic computation methods in information theory and nonlinear systems. He was a recipient of the president award of Chinese Academy of Sciences, and published over 10 papers on information theory and nonlinear system.

邀请人：黄巧龙

时间：2023年3月20日（周一），14:30-15:00

地点：腾讯会议

联系人：黄巧龙 huangqiaolong@sdu.edu.cn