Elimination of epsilon

Question

Question : (Here e=epsilon) S->A|B, A->e, B->aBb, B->b

My answer is :

S->B, B->aBb , B->b

  or

S->B|e , B->aBb , B->b

Want to know which one is correct ? please explain...

Answer 1

second one is correct , if S---> e we could not eliminate it bcoz language generate e ,and if language does not generate e then it can be eliminate ...

s-->AB

A--->aAA/e

B--->bBB/e after elimination of e

S-->AB/A/B/e

A-->aAA/aA/a

B-->bBB/bB/b

Comments

For

S->aS | AB , A->e , A->e

After eliminating epsilon : S->aS | e or S->aS | a

I think both are correct here . just want to make sure..

               

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S-->aS/A/B/AB/a/e ... i thing you miss out B-->e