Grammar

A grammar $G$ is defined as quadruple

$$G = (V, T, S, P),$$

where

• $V$ is a finite set of symbols, called variables.
• $T$ is a finite set of symbols, called terminal tymbols.
• $S\in V$ is a special symbol called start symbol.
• $P$ is finite set of productions.

We always assume that the productions are of the form

$$x \rightarrow y,$$

where $x$ is an element of $(V\cup T)^+$ and $y$ is in $(V\cup T)^*$.