Formal Definition of Context-Free Grammars || Automata Theory

A context free grammar is a method for (recursively) describing the grammar of a given language. A CFG is a set of variables, each of which represents a language. The language, represented by the variables, is described in terms of primitive symbols called Terminals. The rules relating to the variables are called Productions.

A CFG, G, is formally defined as 4-tuple                                                           G=(V, T, P, S) Where V- A finite set of variables or non-terminals.               T- A finite set of terminals.                P- A finite set of production rules.               S- Start symbol, SϵV.

Each production is of the form A ->α, where A is variable, α may be either terminal or non-terminal, i.e., A∈V and α∈ (V ∪ T)