An Automated Theorem Proving Framework for Information-Theoretic Results
Abstract
We present a versatile automated theorem proving framework capable of automated discovery, simplification and proofs of inner and outer bounds in network information theory, deduction of properties of information-theoretic quantities (e.g. Wyner and G\'acs-K\"orner common information), and discovery of non-Shannon-type inequalities, under a unified framework. Our implementation successfully generated proofs for 32 out of 56 theorems in Chapters 1-14 of the book Network Information Theory by El Gamal and Kim. Our framework is based on the concept of existential information inequalities, which provides an axiomatic framework for a wide range of problems in information theory.
Keywords
Cite
@article{arxiv.2101.12370,
title = {An Automated Theorem Proving Framework for Information-Theoretic Results},
author = {Cheuk Ting Li},
journal= {arXiv preprint arXiv:2101.12370},
year = {2022}
}
Comments
27 pages, presented in part at the IEEE International Symposium on Information Theory 2021