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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:
For example, the language = {| >} can be shown to be non-context-free by using the pumping lemma in a proof by contradiction. First, assume that L is context free. By the pumping lemma, there exists an integer p which is the pumping length of language L .
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
Pumping lemma sometimes called the Bar-Hillel lemma; Microeconomics ... An example of a covering described by the Knaster–Kuratowski–Mazurkiewicz lemma.
Despite Ogden's lemma being a strengthening of the pumping lemma, it is insufficient to fully characterize the class of context-free languages. [2] This is in contrast to the Myhill-Nerode theorem , which unlike the pumping lemma for regular languages is a necessary and sufficient condition for regularity.
For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. ... Pumping lemma for regular languages, an alternative ...
For example, in the following grammar, with start symbol S 0, ... Pumping lemma for context-free languages — its proof relies on the Chomsky normal form; Notes
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 ...