The Undecidability of Conditional Affine Information Inequalities and Conditional Independence Implication with a Binary Constraint

Cheuk Ting Li

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arXiv · 2104.05634

The Undecidability of Conditional Affine Information Inequalities and Conditional Independence Implication with a Binary Constraint

Cheuk Ting Li

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Abstract

We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the problem of deciding whether the intersection of the entropic region and a given affine subspace is empty. This is a step towards the conjecture on the undecidability of conditional independence implication. The undecidability is proved via a reduction from the periodic tiling problem (a variant of the domino problem). Hence, one can construct examples of the aforementioned problems that are independent of ZFC (assuming ZFC is consistent).

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Cheuk Ting Li. 2021-04-12. The Undecidability of Conditional Affine Information Inequalities and Conditional Independence Implication with a Binary Constraint. https://arxiv.org/abs/2104.05634

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