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In particular, an alternative containing a useless nonterminal symbol can be deleted from the right-hand side of a rule. Such rules and alternatives are called useless. [24] In the depicted example grammar, the nonterminal D is unreachable, and E is unproductive, while C → C causes a cycle.
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 ...
By deleting in this grammar each ε-rule, unless its left-hand side is the start symbol, the transformed grammar is obtained. [4]: 90 For example, in the following grammar, with start symbol S 0, S 0 → AbB | C B → AA | AC C → b | c A → a | ε. the nonterminal A, and hence also B, is nullable, while neither C nor S 0 is.
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.
The size of a grammar is the sum of the sizes of its production rules, where the size of a rule is one plus the length of its right-hand side. Using g {\displaystyle g} to denote the size of the original grammar, the size blow-up in the worst case may range from g 2 {\displaystyle g^{2}} to 2 2 g {\displaystyle 2^{2g}} , depending on the ...
An unrestricted grammar is a formal grammar = (,,,), where . is a finite set of nonterminal symbols,; is a finite set of terminal symbols with and disjoint, [note 1]; is a finite set of production rules of the form , where and are strings of symbols in and is not the empty string, and
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