Fibonacci自动词的判定算法及其在模式回避中的应用
Decision Algorithms for Fibonacci-Automatic Words, with Applications to Pattern Avoidance
摘要：
我们实现了一个决策过程，回答一类无限的话，可能被称为（缺乏一个更好的名字）“斐波那契自动”的问题。例如，这个类包括著名的斐波那契数列f = 01001010...，态射0 -> 01和1 -> 0的不动点。然后，我们从文献中恢复了许多关于斐波那契词的结果（并改进了其中一些结果），例如关于正方形、立方体、回文等在f中出现的断言。作为该方法的一个应用，我们证明了一个新的结果：存在一个非周期的无限二进制字，它避开了模式x x x^R。这是第一个关于非一致态射的可避免性结果，它被纯机械地证明了。
英文摘要：
We implement a decision procedure for answering questions about a class of infinite words that might be called (for lack of a better name) "Fibonacci-automatic". This class includes, for example, the famous Fibonacci word f = 01001010..., the fixed point of the morphism 0 -> 01 and 1 -> 0. We then recover many results about the Fibonacci word from the literature (and improve some of them), such as assertions about the occurrences in f of squares, cubes, palindromes, and so forth. As an application of our method we prove a new result: there exists an aperiodic infinite binary word avoiding the pattern x x x^R. This is the first avoidability result concerning a nonuniform morphism proven purely mechanically.
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。
