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The pumping lemma is often used to prove that a particular language is non-regular: a proof by contradiction may consist of exhibiting a string (of the required length) in the language that lacks the property outlined in the pumping lemma. Example: The language = {:} over the alphabet = {,} can be shown to be non-regular as follows:
The pumping lemma for context-free languages (called just "the pumping lemma" for the rest of this article) describes a property that all context-free languages are guaranteed to have. The property is a property of all strings in the language that are of length at least p {\displaystyle p} , where p {\displaystyle p} is a constant—called the ...
Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma
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 ...
Hi Jochen Burghardt, the example of a non-regular language given to satisfy the non-generalised Pumping Lemma does not satisfy it. For example the word abc can be pumped down to bc which is not in the given language. This is a deep flaw in the example that cannot be easily fixed - as it relies on m ≥ 1.
The language () = {} defined above is not a context-free language, and this can be strictly proven using the pumping lemma for context-free languages, but for example the language {} (at least 1 followed by the same number of 's) is context-free, as it can be defined by the grammar with = {}, = {,}, the start symbol, and the following ...
Ogden's lemma is often stated in the following form, which can be obtained by "forgetting about" the grammar, and concentrating on the language itself: If a language L is context-free, then there exists some number (where p may or may not be a pumping length) such that for any string s of length at least p in L and every way of "marking" p or more of the positions in s, s can be written as
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