What is Context-Free Grammar?

Context Free Grammar is formal grammar, the syntax or structure of a formal language can be described using context-free grammar (CFG), a type of formal grammar. The grammar has four tuples: (V,T,P,S).

V - It is the collection of variables or nonterminal symbols.
T - It is a set of terminals. 
P - It is the production rules that consist of both terminals and nonterminals.
S - It is the Starting symbol.

A grammar is said to be the Context-free grammar if every production is in the form of :

G -> (V∪T)*, where G ∊ V

• And the left-hand side of the G, here in the example can only be a Variable, it cannot be a terminal.
• But on the right-hand side here it can be a Variable or Terminal or both combination of Variable and Terminal.

Above equation states that every production which contains any combination of the ‘V’ variable or ‘T’ terminal is said to be a context-free grammar.

For example the grammar A = { S, a,b, P,S} having production :

• Here S is the starting symbol.
• {a,b} are the terminals generally represented by small characters.
• P is variable along with S.

S-> aS
S-> bSa

but

a->bSa, or
a->ba is not a CFG as on the left-hand side there is a variable which does not follow the CFGs rule.

In the computer science field, context-free grammars are frequently used, especially in the areas of formal language theory, compiler development, and natural language processing. It is also used for explaining the syntax of programming languages and other formal languages.

Limitations of Context-Free Grammar

Apart from all the uses and importance of Context-Free Grammar in the Compiler design and the Computer science field, there are some limitations that are addressed, that is CFGs are less expressive, and neither English nor programming language can be expressed using Context-Free Grammar. Context-Free Grammar can be ambiguous means we can generate multiple parse trees of the same input. For some grammar, Context-Free Grammar can be less efficient because of the exponential time complexity. And the less precise error reporting as CFGs error reporting system is not that precise that can give more detailed error messages and information.