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

04/12/2021

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by   Cheuk Ting Li, et al.

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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).