We investigate the state complexity of the permutation operation on finite languages. We give a tight bound that is expressed in terms of the longest strings in the unary projection languages. Moreover, we ask how large a minimal automaton could be for a finite language such that the lengths of the strings in the unary projection languages are bounded. Lastly, we look at a restricted class of languages with maximal state complexity and derive a state bound expressed in terms of the state complexity of the input language. This result fits with previous results on restricted classes for binary alphabets.

中文翻译：

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有限语言排列的状态复杂度

我们研究了有限语言置换操作的状态复杂性。我们给出了用一元投影语言中最长字符串表示的紧边界。此外，我们问对于有限语言，最小自动机可以有多大，使得一元投影语言中的字符串长度是有界的。最后，我们查看具有最大状态复杂度的受限语言类别，并推导出以输入语言的状态复杂度表示的状态界限。该结果与之前关于二进制字母表受限类的结果相符。