Theory of computation

Question

Set of all strings over {0,1} containing at most one pair of consecutive 1's.

Give regular expression and equivalent minimized DFA.

Answer 1

Regular expression is:

for a string which doest not contain 11 :   (0+10)*(1+e)

for a string which contain one 11:  (0+10)*(1+e)0110(0+10)*(1+e)

 

and for atmost      :::::::     (0+10)*(1+e) + (0+10)*(1+e)0110(0+10)*(1+e)

Comments

could u pls explain why do u write 0110?

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B/C if i take 11

 (0+10)*(1+e)11(0+10)*(1+e)

in middle 111 can be produce which is violating the condition of atmost one 11

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can ((0+10)*(1+e)0110(0+10)*(1+e)) equation dont give atmost 11  ??

Y there is need for [(0+10)*(1+e) +] in front of that equation..?