论文标题
通用Levenshtein距离的正式语言等轴测组
Isometry groups of formal languages for generalized Levenshtein distances
论文作者
论文摘要
本文是对哪些组可以表示为普遍Levenshtein距离的正式语言等轴测群的部分答案。即，证明，对于任何语言，其单词长度与图像长度之间的差异模量对于任意的广义Levenshtein距离，该距离的距离使替换操作的重量的重量小于删除操作的重量的两倍以上的重量仅在语言本身的常数上界定。特别是从此可以得出的是，相对于此类指标的正式语言组始终嵌入$π_{n = 1}^\ infty s_ {n} $。我们还构建了许多示例，表明从某种意义上说，此估计值是不可解决的。
This article is a partial answer to the question of which groups can be represented as isometry groups of formal languages for generalized Levenshtein distances. Namely, it is proved that for any language the modulus of the difference between the lengths of its words and the lengths of their images under isometry for an arbitrary generalized Levenshtein distance that satisfies the condition that the weight of the replacement operation is less than twice the weight of the removal operation is bounded above by a constant that depends only on the language itself. From this, in particular, it follows that the isometry groups of formal languages with respect to such metrics always embed into the group $Π_{n=1}^\infty S_{n}$. We also construct a number of examples showing that this estimate is, in a certain sense, unimprovable.
