Forbidden Words in Symbolic Dynamics
Forbidden Words in Symbolic Dynamics
复制标题
符号动力学中的禁用词
DOI：
10.1006/aama.2000.0682
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
M. Sciortino
中科院分区：
文献类型：
--
作者：
Marie;F. Mignosi;A. Restivo;M. Sciortino
我们引入一个等价关系？在N到N的函数之间，通过用禁忌词来描述符号动力系统，我们证明？计算系统的最小禁词的函数的等价类是系统的拓扑不变量。我们证明了新的不变量独立于以前的不变量，但它不是特征性的。在计算机系统中，我们证明？相应函数的等价性是一个可判定的问题。作为一个更特殊的应用，我们通过使用新的不变量证明了两个与具有“不同斜率”的Sturmian词相关的系统不是共轭的。
We introduce an equivalence relation?between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the?-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the?-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having “different slope” are not conjugate.