Swapping Lemmas for Regular and Context-Free Languages

Tomoyuki Yamakami

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arXiv · 0808.4122

Swapping Lemmas for Regular and Context-Free Languages

Tomoyuki Yamakami

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Abstract

In formal language theory, one of the most fundamental tools, known as pumping lemmas, is extremely useful for regular and context-free languages. However, there are natural properties for which the pumping lemmas are of little use. One of such examples concerns a notion of advice, which depends only on the size of an underlying input. A standard pumping lemma encounters difficulty in proving that a given language is not regular in the presence of advice. We develop its substitution, called a swapping lemma for regular languages, to demonstrate the non-regularity of a target language with advice. For context-free languages, we also present a similar form of swapping lemma, which serves as a technical tool to show that certain languages are not context-free with advice.

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Tomoyuki Yamakami. 2009-03-05. Swapping Lemmas for Regular and Context-Free Languages. https://arxiv.org/abs/0808.4122

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