Let [Formula: see text] be the minimal number of accepting states which is sufficient for deterministic finite automata to accept [Formula: see text]. For a number [Formula: see text] and an [Formula: see text]-ary regularity preserving operation ∘, we define [Formula: see text] as the set of all integers [Formula: see text] such that there are [Formula: see text] languages [Formula: see text], [Formula: see text], with [Formula: see text] In this paper, we study these sets for the operations union, catenation, star, complement, set-subtraction, and intersection where we restrict to unary or finite or unary and finite languages [Formula: see text].

中文翻译：

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操作接受状态复杂性：一元和有限情况

令 [Formula: see text] 为足以让确定性有限自动机接受 [Formula: see text] 的最小接受状态数。对于一个数 [Formula: see text] 和一个 [Formula: see text]-ary 正则保持操作∘，我们将 [Formula: see text] 定义为所有整数 [Formula: see text] 的集合，使得有 [Formula : see text] 语言 [Formula: see text], [Formula: see text], with [Formula: see text] 在本文中，我们研究这些集合的运算并集、连接、星号、补码、集合减法和我们限制为一元或有限或一元和有限语言的交集[公式：见文本]。