V2EX kleene star

Kleene Star

定义 Definition

Kleene star(克林星号)是形式语言与正则表达式中的运算符,写作 *,表示“对某个模式进行零次或多次重复”。对语言 \(L\) 而言,\(L^*\) 包含把 \(L\) 中字符串重复任意次数(含 0 次得到空串 \(\varepsilon\))后形成的所有字符串。
(在日常正则表达式里也常见,如 a* 匹配空串、aaaaaa 等。)

发音 Pronunciation (IPA)

/klini str/

例句 Examples

a* matches the empty string, a, aa, and aaa.
a* 可以匹配空串、aaaaaa

In automata theory, applying the Kleene star to a regular language yields another regular language.
在自动机理论中,对一个正则语言应用克林星号,得到的仍然是正则语言。

词源 Etymology

“Kleene star”以美国数学家与逻辑学家 Stephen Cole Kleene(斯蒂芬科尔克林)命名。他在 20 世纪中期的形式语言与正则事件(regular events)研中系统化了这一闭包运算;“star(星号)”指其符号 * 的形状与用法。

相关词 Related Words

文学/著作中的用例 Literary Works

  • Stephen C. Kleene, Representation of Events in Nerve Nets and Finite Automata(1956)
  • John E. Hopcroft & Jeffrey D. Ullman, Introduction to Automata Theory, Languages, and Computation
  • Michael Sipser, Introduction to the Theory of Computation
  • Alfred V. Aho, Monica S. Lam, Ravi Sethi, Jeffrey D. Ullman, Compilers: Principles, Techniques, and Tools(“龙书”,正则表达式章节常涉及 *
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