UGC NET CSE | September 2013 | Part 2 | Question: 15

Question

Consider the following two languages:

$L_1 =\{a^n b^l a^k \mid n+l+k > 5\}$

$L_2 =\{a^n b^l a^k \mid n> 5, l>3, k \leq l \}$

Which one of the following is true?

• A. $L_1$ is regular language and $L_2$ is not regular language
• B. Both $L_1$ and $L_2$ are regular language
• C. Both $L_1$ and $L_2$ are not regular language
• D. $L_1$ is not regular language and $L_2$ is regular language

Answer 1

I think A is the answer.

L1 is regular but not L2.

In L2 we have to remember the value of l (no of b's) so that it can be compared with k.

regular grammar cannot remember a value (It has no stack)

Thus it is not regular

 

Correct me if i am wrong!

Comments

yes you are correct.

$L_1 = L(a^*b^*a^*) \cap \{ |w|>5 | w \in (a+b)^* \}$

L1 is regular.

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correct .

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Can u please draw finite automata of L1