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A derivation sequence is a non-empty sequence of sentential forms $\alpha_1$, $\alpha_2$, … $\alpha_{k-1}$, $\alpha_k$ in which consecutive elements of the sequence are derivation steps:

\(\alpha_1 \to \alpha_2 \to \cdots{} \to \alpha_{k-1} \to \alpha_k\)

A sentential form $\beta$ is derivable from $\alpha$, written $\alpha \to^* \beta$ just if there is a derivation sequence starting with $\alpha$ and ending with $\beta$.

The language of a grammar $G$, written $L(G)$, is the set of all strings $w$ consisting only of terminal symbols and which are derivable from the start symbol, i.e. \(\{\, w \mid S \to^* w \,\}\).