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In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form. with a single nonterminal symbol, and a string of terminals and/or nonterminals ( can be empty).
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 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.
Syntax diagrams (or railroad diagrams) are a way to represent a context-free grammar. They represent a graphical alternative to Backus–Naur form, EBNF, Augmented Backus–Naur form, and other text-based grammars as metalanguages. Early books using syntax diagrams include the "Pascal User Manual" written by Niklaus Wirth [1] (diagrams start at ...
Backus–Naur form. In computer science, Backus–Naur form (/ ˌbækəs ˈnaʊər /) (BNF or Backus normal form) is a notation used to describe the syntax of programming languages or other formal languages. It was developed by John Backus and Peter Naur. BNF can be described as a metasyntax notation for context-free grammars.
Extended Backus–Naur form. In computer science, extended Backus–Naur form (EBNF) is a family of metasyntax notations, any of which can be used to express a context-free grammar. EBNF is used to make a formal description of a formal language such as a computer programming language. They are extensions of the basic Backus–Naur form (BNF ...
In computer science, the Cocke–Younger–Kasami algorithm (alternatively called CYK, or CKY) is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. [1][2] The algorithm is named after some of its rediscoverers: John Cocke, Daniel Younger, Tadao Kasami, and Jacob T. Schwartz.
Ambiguous grammar. 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] Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule.