Fourier-Motkzin Elimination software for Information Theory

Fourier-Motzkin Elimination Software for Information Theoretic Inequalities

We provide open-source software implemented in MATLAB, that performs Fourier-Motzkin elimination (FME) and removes constraints that are redundant due to Shannon-type inequalities (STIs). The FME is often used in information theoretic contexts to simplify rate regions, e.g., by eliminating auxiliary rates. Occasionally, however, the procedure becomes cumbersome, which makes an error-free hand-wr...

Extracting analytic proofs from numerically solved Shannon-type Inequalities

A class of information inequalities, called Shannon-type inequalities (STIs), can be proven via a computer software called ITIP [1]. In previous work [2], we have shown how this technique can be utilized to Fourier-Motzkin elimination algorithm for Information Theoretic Inequalities. Here, we provide an algorithm for extracting analytic proofs of information inequalities. Shannon-type inequalit...

Strong Duality and Dual Pricing Properties in Semi-Infinite Linear Programming: A non-Fourier-Motzkin Elimination Approach

The Fourier-Motzkin elimination method has been recently extended to linear inequality systems that have infinitely many inequalities. It has been used in the study of linear semi-infinite programming by Basu, Martin, and Ryan. Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang recently published in Optimization, which states “all the duality res...

Fourier-Motzkin Elimination and Its Dual

Generating facets for the cut polytope of a graph by triangular elimination

The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science requires knowledge of the facets of the cut polytope of the complete bipartite graph or, more generally, the complete k-partite graph. Lifting is a central tool to ...