Question

The grammar $S\to aSa|bS|c$ is

• A. Both LL(1) and LR(1)
• B. LR(1) but not LL(1)
• C. Neither LL(1) nor LR(1)
• D. LL(1) but not LR(1)

Answer 1

The correct option is A Both LL(1) and LR(1)

$S\to aSa|bS|c$
The above grammar is LL(1) because,
$\text{First [aSa]}\cap \text{first [bS]}=\left(a\right)\cap \left(b\right)=\varphi$
&&
$\text{First [bs]}\cap \text{first [c]}=\left(b\right)\cap \left(c\right)=\varphi$
&&
$\text{First [c]}\cap \text{first [aSa]}=\left(c\right)\cap \left(a\right)=\varphi$

As the above grammar is LL(1), also LR(1) because LL(1) grammar is always LR(1) grammar.