Swapping Lemmas for Regular and Context-Free Languages

Tomoyuki Yamakami
Arxiv ID: 808.4122Last updated: 3/5/2009
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.

PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.

Related papers

Commercial Disclosure
© 2023 Paper Studio™. All Rights Reserved.