Search results
Results from the WOW.Com Content Network
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 ...
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.
To convert a grammar to Chomsky normal form, a sequence of simple transformations is applied in a certain order; this is described in most textbooks on automata theory. [4]: 87–94 [5] [6] [7] The presentation here follows Hopcroft, Ullman (1979), but is adapted to use the transformation names from Lange, Leiß (2009).
In the theory of formal languages, Ogden's lemma (named after William F. Ogden) [1] is a generalization of the pumping lemma for context-free languages. 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 ...
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 fact that this language is not context free can be proven using pumping lemma for context-free languages and a proof by contradiction, observing that all words of the form ([)] should belong to the language.
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 term phrase structure grammar was originally introduced by Noam Chomsky as the term for grammar studied previously by Emil Post and Axel Thue (Post canonical systems).Some authors, however, reserve the term for more restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars.