Subshifts are colorings of $\mathbb{Z}^d$ defined by families of forbidden patterns. Given a subshift and a finite pattern, its extender set is the set of admissible completions of this pattern. It has been conjectured that the behavior of extender sets, and in particular their growth called extender entropy (arXiv:1711.07515), could provide a way to separate the classes of sofic and effective subshifts. We prove here that both classes have the same possible extender entropies: exactly the $\Pi_3$ real numbers of $[0,+\infty)$. We also consider computational properties of extender entropies for subshifts with some language or dynamical properties: computable language, minimal and some mixing properties.

翻译：子移位是由禁止模式族定义的 $\mathbb{Z}^d$ 着色。给定一个子移位及其有限模式，其扩展子集合是该模式的可接受补全集合。已有猜想认为，扩展子集合的行为，特别是其增长（称为扩展子熵，见arXiv:1711.07515），可能为区分sofic子移位与有效子移位类别提供途径。本文证明这两类子移位具有相同的可能扩展子熵：恰好为 $[0,+\infty)$ 中的 $\Pi_3$ 实数。我们还考虑了具有某些语言或动力学性质的子移位（可计算语言、极小性及若干混合性质）的扩展子熵的计算特性。