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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.
Some do not permit the second form of rule and cannot transform context-free grammars that can generate the empty word. For one such construction the size of the constructed grammar is O(n 4) in the general case and O(n 3) if no derivation of the original grammar consists of a single nonterminal symbol, where n is the size of the original ...
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 ...
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]
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