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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 ...
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 ...
In theoretical computer science and formal language theory, a regular language (also called a rational language) [1] [2] is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages).
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 regular languages, the fact that all sufficiently long strings in such a language have a substring that can be repeated arbitrarily many times, usually used to prove that certain languages are not regular; Pumping lemma for context-free languages, the fact that all sufficiently long strings in such a language have a pair of ...
Proof on deterministic finite automaton to regular expression; pumping lemma for regular languages; Topics on context-free language include: pushdown automata; context-free grammar; proof on wikt:nondeterministic pushdown automaton to context-free grammar; proof on context-free grammar to pushdown automaton; pumping lemma for context-free ...
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)
An extended context-free grammar (or regular right part grammar) is one in which the right-hand side of the production rules is allowed to be a regular expression over the grammar's terminals and nonterminals. Extended context-free grammars describe exactly the context-free languages.