Formal definitions of a Grammar

A grammar G is defined as a quadruple.

N is a non-empty finite set of non-terminals or variables,

is a non-empty finite set of terminal symbols such that

, is a special non-terminal (or variable) called the start symbol, and is a finite set of production rules.

The binary relation defined by the set of production rules is denoted by , i.e. iff .

In other words, P is a finite set of production rules of the form , where and