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# GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 24

• Last Updated : 20 Dec, 2019

Both Mr. Mithlesh Upadhyay and You play a game:

1. Mr. Mithlesh Upadhyay gives you a constant n.
2. You choose a word w in the language of length at least n.
3. Mr. Mithlesh Upadhyay gives you x, y, and z with xyz = w, |xy|≤n, and y not empty.
4. Now you pick r.
5. Mr. Mithlesh Upadhyay asserts that xyrz is also in the language.
6. If Mr. Mithlesh Upadhyay is wrong, you win.

In case, if you win the game, what is the minimum possible value of your r for the language {0i1j | i >= j} ?
(A) 0
(B) 2
(C) 3
(D) Mr. Mithlesh Upadhyay won the game for given language.

Explanation: Given, above game is known as Pumping Lemma for regular languages.

You won the game for the minimum value of r is 0.

Option (A) is correct.

Quiz of this Question

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