GATE | GATE-CS-2015 (Set 2) | Question 61

Which of the following languages is/are regular?

L1: {wxwR ⎪ w, x ∈ {a, b}* and ⎪w⎪, ⎪x⎪ >0} wR is the reverse of string w
L2: {anbm ⎪m ≠ n and m, n≥0
L3: {apbqcr ⎪ p, q, r ≥ 0}  

(A) L1 and L3 only
(B) L2 only
(C) L2 and L3 only
(D) L3 only


Answer: (A)

Explanation:

L3 is simple to guess, it is regular.
Below is DFA for L1.



L1 is interesting. The important thing to note 
about L1 is length of x is greater than 0, i.e.,
|x| > 0.
So any string than starts and ends with same character
is acceptable by language and remaining string becomes w.
Below is DFA for L1.

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