自动序列的临界指数是可计算的
The Critical Exponent is Computable for Automatic Sequences
摘要：
无限字的临界指数被定义为它的每个因子的指数的上确界。对于k-自动序列，我们证明了这个临界指数总是有理数或无穷大，并且它的值是可计算的。我们的结果也适用于变种的临界指数，如初始临界指数的Berthe，Holton，和Zamboni和丢番图指数的Adamczewski和Bugeaud。我们的工作推广或恢复了Krieger和其他人以前的结果，并适用于其他情况;例如，线性递归k-自动序列的最优递归常数的计算。
英文摘要：
The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.
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