Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication

Cheuk Ting Li

doi:10.1109/tit.2023.3247570

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arXiv · 2205.11461

Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication

Cheuk Ting Li

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Abstract

We resolve three long-standing open problems, namely the (algorithmic) decidability of network coding, the decidability of conditional information inequalities, and the decidability of conditional independence implication among random variables, by showing that these problems are undecidable. The proof utilizes a construction inspired by Herrmann's arguments on embedded multivalued database dependencies, a network studied by Dougherty, Freiling and Zeger, together with a novel construction to represent group automorphisms on top of the network.

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Cheuk Ting Li. 2022-05-23. Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication. https://doi.org/10.1109/tit.2023.3247570

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