A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language transformation algorithms in terms of modifier and monster. These new theoretical concepts allow one to find easily some state complexities. We illustrate this by retrieving the state complexity of the Star of Intersection and the one of the Square root operation.

中文翻译：

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状态复杂性的新工具

怪物是一种自动机，其中从状态到状态的每个功能都由至少一个字母表示。修饰符是一组函数，允许将一组自动机转换为一个自动机。我们重新审视了一些关于修饰符和怪物的语言转换算法。这些新的理论概念使人们可以轻松找到一些状态复杂性。我们通过检索交点星的状态复杂度和平方根运算之一来说明这一点。