What is a Context-Free Grammar?
A context-free grammar (CFG) is a set of rewriting rules (or productions) used to generate patterns of strings. A CFG consists of a set of terminal symbols, which are the characters of the alphabet that appear in the strings generated by the grammar, and a set of nonterminal symbols, which are placeholders for patterns of characters. The rules of a CFG specify how the nonterminal symbols can be rewritten as strings of terminal symbols.
Format of a Context-Free Grammar
A context-free grammar (CFG) consists of a set of production rules. A production rule has two parts: a left-hand side (LHS) and a right-hand side (RHS). The LHS is a single non-terminal symbol, and the RHS is a string of zero or more terminals and/or non-terminals. For example, consider the following production rule:
S → AB
This rule says that the non-terminal S can be replaced by the string AB.
Examples of Context-Free Grammars
A context-free grammar (CFG) is a set of rewriting rules (or productions) used to generate patterns of strings. A CFG consists of a finite set of terminal symbols, which are the characters that can appear in the generated strings, and a finite set of nonterminal symbols, which are placeholders for patterns that can be generated from other symbols in the grammar. The rules of a CFG specify how the nonterminals can be rewritten as strings of terminals and other nonterminals.
Here are some examples of context-free grammars:
- The grammar {::= } generates all HTML documents with a head followed by a body.
- The grammar {
::= } generates all English sentences consisting of a noun phrase followed by a verb phrase. - The grammar {
::= | } generates all English sentences consisting of a noun phrase followed by either a verb phrase or a prepositional phrase. - The grammar {::={0,1,2,3,4,5,6,7,8,9}} generates all decimal numbers from 0 to 9.
Uses of Context-Free Grammars
Context-free grammars have many applications in computer science. Perhaps the most popular is in parsing, where a context-free grammar can be used to describe the syntax of a programming language or document format. once a context-free grammar has been designed for a particular syntax, a parser can be automatically generated from it that will check whether strings match the grammar (i.e., whether they are syntactically valid according to the grammar) and, if so, will build a parse tree showing the structure of the string according to the grammar. Context-free grammars are also used in systems for automatic speech recognition and machine translation