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A formal language defined or generated by a particular grammar is the set of strings that can be produced by the grammar and that consist only of terminal symbols. Diagram 1 illustrates a string that can be produced with this grammar. Diagram 1. The string Б Б Б Б was formed by the grammar defined by the given production rules. This grammar ...
A context-sensitive grammar is a noncontracting grammar in which all rules are of the form αAβ → αγβ, where A is a nonterminal, and γ is a nonempty string of nonterminal and/or terminal symbols. However, some authors use the term context-sensitive grammar to refer to noncontracting grammars in general. [1]
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.
Let us notate a formal grammar as = (,,,), with a set of nonterminal symbols, a set of terminal symbols, a set of production rules, and the start symbol.. A string () directly yields, or directly derives to, a string (), denoted as , if v can be obtained from u by an application of some production rule in P, that is, if = and =, where () is a production rule, and , is the unaffected left and ...
It is named after Sige-Yuki Kuroda, who originally called it a linear bounded grammar, a terminology that was also used by a few other authors thereafter. [ 3 ] Every grammar in Kuroda normal form is noncontracting , and therefore, generates a context-sensitive language .
Every regular grammar is context-free, but not all context-free grammars are regular. [10] The following context-free grammar, for example, is also regular. S → a S → aS S → bS. The terminals here are a and b, while the only nonterminal is S.
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.
Gerald Gazdar has defined a second class, the linear indexed grammars (LIG), [14] by requiring that at most one nonterminal in each production be specified as receiving the stack, [note 2] whereas in an ordinary indexed grammar, all nonterminals receive copies of the stack. Formally, a linear indexed grammar is defined similar to an ordinary ...
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