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6. [5 points] Let Lo be the language over { = {0,1} consisting of strings having twice as many Os as it has l’s. For example

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Answer #1

pumping lemma for regular languages:

1)assume given language is regular and there exist a finite automata with 2k states.

2)take a valid string z from L.

z=001010

3)divide the string z into 3 parts,U,V,W in such a way that |V|>=1 and |UV|<=2k

U=0010

V=1

W=0

4)if for any value of i, UVIW belongs to L then L is regular otherwise L is not regular.

say i=2 then UViW becomes 0010110 this is not belongs to L

this is contradiction to given statement.

therefore L is not regular.

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