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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. [9]
The general idea of a hierarchy of grammars was first described by Noam Chomsky in "Three models for the description of language". [1] Marcel-Paul Schützenberger also played a role in the development of the theory of formal languages; the paper "The algebraic theory of context free languages" [2] describes the modern hierarchy, including context-free grammars.
Deterministic context-free languages can be recognized by a deterministic Turing machine in polynomial time and O(log 2 n) space; as a corollary, DCFL is a subset of the complexity class SC. [3] The set of deterministic context-free languages is closed under the following operations: [4] complement; inverse homomorphism; right quotient with a ...
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. [1] [2] Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule.
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 ...
This language is nondeterministic. Since nondeterministic context-free languages cannot be accepted in linear time [clarification needed], linear languages cannot be accepted in linear time in the general case. Furthermore, it is undecidable whether a given context-free language is a linear context-free language. [2]
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.