有条件的对等信息不平等和有条件的独立与二进制限制不相适应的不可减轻性 (The Undecidability of Conditional Affine Information Inequalities and Conditional Independence Implication with a Binary Constraint)

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).

翻译：我们确定了有条件的同系物信息不平等的不可减损性,有条件的独立隐含问题的不可减损性,但有一项制约,即一个随机变量是二进制的,以及决定昆虫区域和给定的同系物子空间的交叉点是否是空的这一问题的不可减损性。这是对有条件的独立隐含的不可减损性的推断的一个步骤。通过减少周期性平铺问题(多米诺问题的一个变式),可以证明不失效性。因此,可以建立上述问题独立于ZFC(假设ZFC是一致的)的例子。