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An extended context-free grammar (or regular right part grammar) is one in which the right-hand side of the production rules is allowed to be a regular expression over the grammar's terminals and nonterminals. Extended context-free grammars describe exactly the context-free languages.
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.
Deterministic context-free grammars were particularly useful because they could be parsed sequentially by a deterministic pushdown automaton, which was a requirement due to computer memory constraints. [4] In 1965, Donald Knuth invented the LR(k) parser and proved that there exists an LR(k) grammar for every deterministic context-free language. [5]
Generalized context-free grammar (GCFG) is a grammar formalism that expands on context-free grammars by adding potentially non-context-free composition functions to rewrite rules. [1] Head grammar (and its weak equivalents) is an instance of such a GCFG which is known to be especially adept at handling a wide variety of non-CF properties of ...
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.
A weighted context-free grammar (WCFG) is a more general category of context-free grammar, where each production has a numeric weight associated with it. The weight of a specific parse tree in a WCFG is the product [7] (or sum [8]) of all rule weights in the tree. Each rule weight is included as often as the rule is used in the tree.
Synchronous context-free grammars (SynCFG or SCFG; not to be confused with stochastic CFGs) are a type of formal grammar designed for use in transfer-based machine translation. Rules in these grammars apply to two languages at the same time, capturing grammatical structures that are each other's translations.
The phrase grammar of most programming languages can be specified using a Type-2 grammar, i.e., they are context-free grammars, [8] though the overall syntax is context-sensitive (due to variable declarations and nested scopes), hence Type-1. However, there are exceptions, and for some languages the phrase grammar is Type-0 (Turing-complete).
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