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In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped —that is, have a middle section of the string repeated an arbitrary number of times—to produce a new ...
Pumping lemma for regular languages, an alternative method for proving that a language is not regular. The pumping lemma may not always be able to prove that a language is not regular. The pumping lemma may not always be able to prove that a language is not regular.
Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair of substrings that can be repeated arbitrarily many times, usually used to prove that certain languages are not context-free; Pumping lemma for indexed languages; Pumping lemma for regular tree languages
The converse is not true: for example, the language consisting of all strings having the same number of a's as b's is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma .
In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, [1] is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages. The pumping lemma can be used to construct a refutation by ...
Illustration of the pumping lemma for regular automata Chomsky and Miller (1957) [ 15 ] used the pumping lemma : they guess a part v of an input string uvw and try to build a corresponding cycle into the automaton to be learned; using membership queries they ask, for appropriate k , which of the strings uw , uvvw , uvvvw , ..., uv k w also ...
The pumping lemma can't be used to prove that a given Language L is regular, since it provides a necessary, but not sufficient condition for regularity; cf. the "⇒" after "regular(L)" in the formal expression, and section Pumping_lemma_for_regular_languages#Converse_of_lemma_not_true. - Jochen Burghardt 08:47, 14 June 2023 (UTC)
The language is context-free but not regular (by the pumping lemma for regular languages). Context-sensitive (Type-1) grammars Type-1 ...