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Context-free grammars are a special form of Semi-Thue systems that in their general form date back to the work of Axel Thue. The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, [3] and also their classification as a special type of formal grammar (which he called phrase-structure grammars). [4]
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 PDA accepts by empty stack. Its initial stack symbol is the grammar's start symbol. [3] For a context-free grammar in Greibach normal form, defining (1,γ) ∈ δ(1,a,A) for each grammar rule A → aγ also yields an equivalent nondeterministic pushdown automaton. [2]: 115 The converse, finding a grammar for a given PDA, is not that easy.
A lookahead LR parser (LALR) generator is a software tool that reads a context-free grammar (CFG) and creates an LALR parser which is capable of parsing files written in the context-free language defined by the CFG. LALR parsers are desirable because they are very fast and small in comparison to other types of parsers.
The standard version of CYK operates only on context-free grammars given in Chomsky normal form (CNF). However any context-free grammar may be algorithmically transformed into a CNF grammar expressing the same language (Sipser 1997). The importance of the CYK algorithm stems from its high efficiency in certain situations.
Context-free grammar (CFGs) are used in programming languages and artificial intelligence. Originally, CFGs were used in the study of human languages. Cellular automata are used in the field of artificial life, the most famous example being John Conway's Game of Life. Some other examples which could be explained using automata theory in biology ...
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.
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 ...
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