Which of the following are regular sets?
(A)
{anb2m|n≥0, m≥0}
(B)
{anbm | n = 2m}
(C)
{anbm n≠m}
(D)
{xcy | x,y ∈ {a,b}*}
Answer: (A) (D)
Explanation:
1.L = {a n b 2m |m, n ≥ 0} is a regular language of the form a ∗ (bb) ∗ .
2.L = {a n b m |n = 2m} is not a regular language. This is a similar language as of {a n b n } which is known to be not a regular language.
3. L = {a n b m |n notEqualTo m} is not regular because there is no way to for finite automaton to remember n, number of as.
4. L = {xcy|x, y ∈ {a, b} ∗ } is a regular language which is concatenation of {x|x ∈ a, b ∗ } on itself with a alphabet c in between.
Note: Regular languages are closed under concatenation.
Hence, correct answer would be I and IV only.
Quiz of this Question
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