星高
在数学里，正则表示法E在有限字母A的星高h（E）定义如下：:
- h(∅) = 0, h(ε) = 0, h（a）= 0, ∀ a ∈ A.
- h(E ∪ F) = h（EF）= max(h（E）, h（F）)
- h(E) = h（E）
- h(E) = h（E）+ 1
正则语言L的星高定义为所有能表示L的正则表达式的星高的最小值。
可证明，语言L有星高0 若且唯若其语法zh-cn:幺半群为非周期幺半群。
Star height
中文百科
英语百科
Star height 星高
![Example automaton of cycle rank 1. Kleene's algorithm transforms it into the regular expression a*b*ba
((a|b)b*a|ε)* (a|b)b* | a*b*b, which has star-height 2. By Eggan's theorem, an equivalent regular expression of star-height ≤1 must exist. In fact, a*b(b|a(a|b))* describes the same language.](/Images/godic/202502/13/Deterministicfiniteautomaton.svg4715.png")
In theoretical computer science, more precisely in the theory of formal languages, the star height is a measure for the structural complexity of regular expressions: The star height equals the maximum nesting depth of stars appearing in the regular expression. The concept of star height was first defined and studied by Eggan (1963).
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