concatenation of regular and DCFL

Rajesh R 09/22/2018 at 08:26. 0 answers, 0 views

$S -> AB$

$A -> aA / epsilon$

$B ->aBb / epsilon$

What is the class of language generated by the above grammar ?

I think that it generates $a^* a^n b^n | n>=0$ so it should be regular as regular is concatenated with DCFL which is able generate epsilon. But the answer is CFL .

I think that answer would be CFL if n would have been greater than equal to 1 and not 0

Can someone please point out my mistake ?

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