Context free grammar
Context free grammar is a formal grammar which is used to generate all possible strings in a given formal language.
Context free grammar G can be defined by four tuples as:
Where,
G describes the grammar
T describes a finite set of terminal symbols.
V describes a finite set of non-terminal symbols
P describes a set of production rules
S is the start symbol.
In CFG, the start symbol is used to derive the string. You can derive the string by repeatedly replacing a non-terminal by the right hand side of the production, until all non-terminal have been replaced by terminal symbols.
Example:
Production rules:
Now check that abbcbba string can be derived from the given CFG.
By applying the production S → aSa, S → bSb recursively and finally applying the production S → c, we get the string abbcbba.