An Automated Theorem Proving Framework for Information-Theoretic Results

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 Gács-Körner 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.