The equivalent grammar corresponding to the grammar S → aA A → BB B → aBb | ε

First, identify nullable non-terminals. B is nullable due to the production B → ε. Since A → BB, A becomes nullable if both B's derive empty strings. Eliminate epsilon productions. For B → aBb | ε, add the production B → ab where the inner B is removed. Update A to include single B: A → BB | B. Update S since A is nullable. Add the production S → a. The resulting grammar without epsilon productions preserves the original language.