有理数基数系统中的自相似性
摘要：整数在有理数基数系统中的表示集合的研究 contributor这项工作是对整数在有理数基数系统中的表示集合研究的一个贡献 （This work is a contribution to the study of set of the representations of integers in a rational base number system.） 该自由单子前缀闭子集可以自然地表示为一个高度非规则的树，其节点是整数，其子树都不同。 （This prefix-closed subset of the free monoid is naturally represented as a highly non regular tree whose nodes are the integers and whose subtrees are all distinct.） 然后，与该树的每个节点相关联一个最小无限词。 （With every node of that tree is then associated a minimal infinite word.） 主要的结果是，顺序传输器从与n相关联的最小词计算与n+1相关联的最小词时，其基本图与树本身基本相同。 （The main result is that a sequential transducer which computes for all n the minimal word associated with n+1 from the one associated with n, has essentially the same underlying graph as the tree itself.） 然后，将这些无限词解释为实数的表示；由这两个连续的最小词所表示的数字之间的差异称为树的一个节点的跨度。 （These infinite words are then interpreted as representations of real numbers; the difference between the numbers represented by these two consecutive minimal words is the called the span of a node of the tree.） 前述的构造允许表征该跨度集合的拓扑闭包。 （The preceding construction allows to characterise the topological closure of the set of spans.）
作者：Shigeki Akiyama and Victor Marsault and Jacques Sakarovitch
论文ID：1305.6757
分类：Formal Languages and Automata Theory
分类简称：cs.FL
提交时间：2013-05-30