We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

中文翻译：

---

替代系统和 Cobham 定理的有限版本

我们研究了由非原始替代产生的替代系统，并表明替代系统的传递子系统是替代的。作为一个应用程序，我们获得了单词集的完整特征，这些单词集可以作为在乘法独立基上定义的两个自动序列的公因子出现。这概括了著名的 Cobham 定理。