论文标题
关于谎言复杂性及以后的注释
A note on the Lie complexity and beyond
论文作者
论文摘要
在最近的一篇论文中，杰森·贝尔（Jason P. Bell）和杰弗里（Jeffrey）Shallit介绍了{\ em Like Complextity}的概念，并证明了自动序列的谎言复杂性函数是自动的。在本说明中，我们提供了更多有关谎言复杂性的事实，并定义了扩展的谎言复杂性和前缀谎言的复杂性。此外，我们证明了一些谎言复杂性也可以使扩展的谎言复杂性保持不变。特别是，我们证明了自动序列的前缀谎言谎言复杂性函数的扩展谎言复杂性函数和一阶差异序列都是自动的。
In a recent paper, Jason P. Bell and Jeffrey Shallit introduced the notion of {\em Lie complexity} and proved that the Lie complexity function of an automatic sequence is automatic. In this note, we give more facts concerning Lie complexity and define the extended Lie complexity and the prefix Lie complexity. Further, we prove that some proprieties of Lie complexity also hold for the extended Lie complexity. Particularly, we prove that the extended Lie complexity function and the first-order difference sequence of the prefix Lie complexity function of an automatic sequence are both automatic.
