理想语言的商复杂度
Quotient complexity of ideal languages
摘要：
本文研究了理想语言类中正则运算的状态复杂性。一个字母表Sigma上的语言L是一个右（左）理想，如果它满足L = L Sigma*（L = Sigma* L）。如果L = Sigma* L Sigma *，则它是双边理想;如果它是Sigma* 与L的混洗，则它是全面理想。我们更喜欢术语“商复杂度”而不是“状态复杂度”，并且只要方便，我们就使用导数来计算商复杂度的上界。我们发现严格的上界商的复杂性的每一种类型的理想语言的复杂性的任意生成器和其最小生成器，最小生成器的复杂性，也对操作的联盟，交叉，集差，对称差，连接，明星和逆转的理想语言。
英文摘要：
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *, and an all-sided ideal if it is the shuffle of Sigma* with L. We prefer the term "quotient complexity" instead of "state complexity", and we use derivatives to calculate upper bounds on quotient complexity, whenever it is convenient. We find tight upper bounds on the quotient complexity of each type of ideal language in terms of the complexity of an arbitrary generator and of its minimal generator, the complexity of the minimal generator, and also on the operations union, intersection, set difference, symmetric difference, concatenation, star and reversal of ideal languages.
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。
