Problem on empty string

Question

Give an algorithm that, given a grammar G = (V, Σ, R, S), decides whether the grammar G can derive the empty string.

Answer 1

Suppose that ^ does not belongs to L(G).

We use the algorithms for removing useless symbols and productions. If S is found to be useless, then L(G) is empty; if not, then L(G) contains at least one element.