Consider the following languages over the alphabet $\sum = \{0, 1, c\}$
$L_1 = \left\{0^n1^n\mid n \geq 0\right\}$
$L_2 = \left\{wcw^r \mid w \in \{0,1\}^*\right\}$
$L_3 = \left\{ww^r \mid w \in \{0,1\}^*\right\}$
Here, $w^r$ is the reverse of the string $w$. Which of these languages are deterministic Context-free languages?
L3 is Non deterministic CFL ...
C.
$L_3$ is CFL and not DCFL as in no way we can deterministically determine the MIDDLE point of the input string.
As c belongs to the input alphabet, it is used to determine the middle part of the string. for example 110c011 is in the language L2. every element is pushed to the stack untill a c occurs. Then the pda changes state and the popping starts.
For the languages L1 & L2 we can have deterministic push down automata, so they are DCFL’s, but for L3 only non-deterministic PDA possible. So the language L3 is not a deterministic CFL.