The language $L=\left\{0^i21^i \mid i \geq 0\right\}$ over the alphabet $\left\{0, 1, 2\right\}$ is:
not recursive
is recursive and is a deterministic CFL
is a regular language
is not a deterministic CFL but a CFL
$L=\left\{0^i21^i \mid i \geq 0\right\}$ has only one comparison that can be done using a DPDA. Hence, its DCFL.
Context free languages are a proper subset of Recursive Languages. $\therefore$ it is recursive too.
answer = option B
L = {0^{i}21^{i} | i>=0 } is deterministic CFL,
Evert DCFL is recursive. As we have membership algorithm for DCFL (Or say CFL in general) , that's why it is recursive. In fact DCFL is subset of Recursive Languages.
SO answer :-
B
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