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Terminal symbols are the elementary symbols of the language defined as part of a formal grammar. Nonterminal symbols (or syntactic variables) are replaced by groups of terminal symbols according to the production rules. The terminals and nonterminals of a particular grammar are in two completely separate sets.
A nonterminal symbol is called productive, or generating, if there is a derivation for some string of terminal symbols. X {\displaystyle X} is called reachable if there is a derivation S ⇒ ∗ α X β {\displaystyle S{\stackrel {*}{\Rightarrow }}\alpha X\beta } for some strings α , β {\displaystyle \alpha ,\beta } of nonterminal and ...
It also distinguishes a special nonterminal symbol, called the start symbol. The language generated by the grammar is defined to be the set of all strings without any nonterminal symbols that can be generated from the string consisting of a single start symbol by (possibly repeated) application of its rules in whatever way possible.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
F is a set of so-called index symbols, or indices, S ∈ N is the start symbol, and; P is a finite set of productions. In productions as well as in derivations of indexed grammars, a string ("stack") σ ∈ F * of index symbols is attached to every nonterminal symbol A ∈ N, denoted by A[σ]. [note 1] Terminal symbols may not be followed by ...
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.
A terminal symbol, such as a word or a token, is a stand-alone structure in a language being defined. A nonterminal symbol represents a syntactic category, which defines one or more valid phrasal or sentence structure consisted of an n-element subset. Metasymbols provide syntactic information for denotational purposes in a given metasyntax.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.