As a variant of the equal entropy cover problem, we ask whether all multidimensional sofic shifts with countably many configurations have SFT covers with countably many configurations. We answer this question in the negative by presenting explicit counterexamples. We formulate necessary conditions for a vertically periodic shift space to have a countable SFT cover, and prove that they are sufficient in a natural (but quite restricted) subclass of shift spaces.

中文翻译：

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具有周期方向的可数Sofic移位

作为等熵覆盖问题的一个变体，我们问是否所有具有许多配置的多维声速位移都具有具有许多配置的SFT覆盖。通过给出明确的反例，我们否定地回答了这个问题。我们为垂直周期的移位空间制定了必要的条件，以使其具有可数的SFT覆盖率，并证明它们在移位空间的自然（但非常受限制）子类中是足够的。