无星整数集的一个特征
Towards a characterization of the star-free sets of integers
摘要：
设U是一个数制，一个整数集合X是U-无星的，如果由X中元素的U-表示构成的集合是一个无星的正则语言。提出了一个关于A. de Luca和A. Restivo，我们得到了一个完整的逻辑表征的U-星免费的整数集的适当的记数系统有关的Pisot数，特别是整数基系统。对于后者的系统，我们研究以及基地的依赖性的问题。最后，还研究了k-adic系统的情形。
英文摘要：
Let U be a numeration system, a set X of integers is U-star-free if the set made up of the U-representations of the elements in X is a star-free regular language. Answering a question of A. de Luca and A. Restivo, we obtain a complete logical characterization of the U-star-free sets of integers for suitable numeration systems related to a Pisot number and in particular for integer base systems. For these latter systems, we study as well the problem of the base dependence. Finally, the case of k-adic systems is also investigated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
