GATE CSE 2001 | Question: 2.6

Question

Consider the following languages:

• $L1=\left\{ww \mid w \in \{a,b\}^*\right\}$
• $L2=\left\{ww^R \mid w \in \{a,b\}^*, w^R \text{ is the reverse of w} \right\}$
• $L3=\left\{0^{2i} \mid \text{ i is an integer} \right\}$
• $L4= \left\{ 0^{i^2} \mid \text{ i is an integer} \right\}$

Which of the languages are regular?

• A. Only $L1$ and $L2$
• B. Only $L2, L3$ and $L4$
• C. Only $L3$ and $L4$
• D. Only $L3$

Comments

L3: By default, we have to assume i is a positive integer(including 0) as the number of zeros(string length) can never be negative.

Answer 1

$$O^{2i}$$

                                                                                            Can be Written as

$$OO^{i}$$

                                                                                           and i can be any positive integer

                                                                                           Therefore Option D is correct