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Applying the rules recursively to a source string of symbols will usually terminate in a final output string consisting only of terminal symbols. Consider a grammar defined by two rules. In this grammar, the symbol Б is a terminal symbol and Ψ is both a non-terminal symbol and the start symbol. The production rules for creating strings are as ...
The language generated by a grammar is the set of all strings of terminal symbols that can be derived, by repeated rule applications, from some particular nonterminal symbol ("start symbol"). Nonterminal symbols are used during the derivation process, but do not appear in its final result string.
Terminals in a grammar are words and through the grammar rules a non-terminal symbol is transformed into a string of either terminals and/or non-terminals. The above grammar is read as "beginning from a non-terminal S the emission can generate either a or b or ". Its derivation is:
The symbols and represent strings of terminal and/or non-terminal symbols, and any non-terminal symbol in either must have an empty stack, by the definition of a LIG. This is, of course, counter to how IGs are defined: in an IG, the non-terminals whose stacks are not being pushed to or popped from must have exactly the same stack as 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]
S is called the start symbol. In a left-regular grammar, (also called left-linear grammar), all rules obey the forms A → a; A → Ba; A → ε; The language described by a given grammar is the set of all strings that contain only terminal symbols and can be derived from the start symbol by repeated application of production rules.
For example, a grammar for a context-free language is left-recursive if there exists a non-terminal symbol A that can be put through the production rules to produce a string with A as the leftmost symbol. [15] An example of recursive grammar is a clause within a sentence separated by two commas. [16]
where A, B, and C are nonterminal symbols, the letter a is a terminal symbol (a symbol that represents a constant value), S is the start symbol, and ε denotes the empty string. Also, neither B nor C may be the start symbol, and the third production rule can only appear if ε is in L(G), the language produced by the context-free grammar G.