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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.
The language is context-free; however, it can be proved that it is not regular. If the productions S → a, S → b, are added, a context-free grammar for the set of all palindromes over the alphabet { a, b} is obtained. [8]
All linear languages are context-free; conversely, an example of a context-free, non-linear language is the Dyck language of well-balanced bracket pairs. Hence, the regular languages are a proper subset of the linear languages, which in turn are a proper subset of the context-free languages.
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language.
The representation of a grammar is a set of syntax diagrams. Each diagram defines a "nonterminal" stage in a process. There is a main diagram which defines the language in the following way: to belong to the language, a word must describe a path in the main diagram. Each diagram has an entry point and an end point.
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).
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 ...
Jump to content. Main menu. Main menu. ... Context-free may refer to: Context-free grammar. ... Deterministic context-free language; See also