equal number of sequence, is language regular ?

Question

L1= Set of all strings having equal number of 00 and 11.
L2= Set of all strings having equal number of 01 and 10.
(a) Both are Regular (b) Both are Context-Free
(c) L1 is regular, L2 is Context Free (d) L1 is CF, L2 is Regular

Answer 1

L1 is well known Non Regular i.e. (00)^n(11)^n. (Since there is no common character in "00" and "11" we need to keep count of both which is not possible with a finite automata as count can be infinite).

L2 is regular and its regular Expression like 0(0+1)*0 + 1(1+0)*1 + 1 + 0 +epsilon.

Comments

can you give an example in which a common character is present and is regular?

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For L2 , according to the given answer it accept string 0, 00 etc. But 0, 00 doesn't belongs to language L2.

Then how can we say that L2 is regular.

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@Digvijay  we cannot generate 01101001 with your regular expression....so i think that it is not a valid regex

Answer 2

this prob is solved before .

ans will be d)

L2 can be considered as all of the stings start and with same elements (0 or 1  )

Comments

can u share the link, where it was solved previously.