广义Levenshtein距离的形式语言的Isometry群
Isometry groups of formal languages for generalized Levenshtein distances
摘要：
本文部分回答了哪些群可以表示为形式语言的等距群的问题。也就是说，它被证明，对于任何语言的词的长度和它们的图像的长度之间的差的模在等距的任意广义Levenshtein距离，满足的条件，即替换操作的重量是小于两倍的重量的删除操作是由一个常数，只取决于语言本身的上界。由此，特别地，可以得出关于这种度量的形式语言的等距群总是嵌入到群$Π_{n=1}^\infty S_{n}$中。我们还构造了一些例子，表明这种估计是，在某种意义上，不可改进的。
英文摘要：
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.
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。
