Pumping lemma

最新推荐文章于 2024-09-23 16:50:16 发布

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最新推荐文章于 2024-09-23 16:50:16 发布

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原文链接：http://www.cnblogs.com/threef/p/3250846.html

本文介绍了计算理论中形式语言的泵引理，包括正则语言及上下文无关语言的泵引理。泵引理是一种重要的工具，用于证明特定语言不属于某语言类。文中详细解释了如何使用这些泵引理，并提供了相关的参考文献。

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In the theory of formal languages in computability theory, a pumping lemma or pumping argument states that, for a particular language to be a member of a language class, any sufficiently long string in the language contains a section, or sections, that can be removed, or repeated any number of times, with the resulting string remaining in that language. The proofs of these lemmas typically require counting arguments such as the pigeonhole principle.

The two most important examples are the pumping lemma for regular languages and the pumping lemma for context-free languages. Ogden's lemmais a second, stronger pumping lemma for context-free languages.

These lemmas can be used to determine if a particular language is not in a given language class. However, they cannot be used to determine if a language is in a given class, since satisfying the pumping lemma is a necessary, but not sufficient, condition for class membership.

References[edit source | editbeta]

Michael Sipser (1997). Introduction to the Theory of Computation. PWS Publishing. ISBN 0-534-94728-X. Section 1.4: Nonregular Languages, pp. 77–83. Section 2.3: Non-context-free Languages, pp. 115–119.
Thomas A. Sudkamp (2006). Languages and Machines, Third edition. Adison Wesley. ISBN 0-321-32221-5. Chapter 6: Properties of Regular Languages pp. 205–210

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