theory of computation

Question

Find the number of states in the minimal DFA over sigma = {0,1} which accepts strings when interpreted as a binary number is divisible by 2.

MY ANSWER :

 

.

But the problem here is it also accepts epsilon . Epsilon is not divisible by 2 right ??? please clear this ...

Comments

Why not 0 divisible by 2 i.e. $\frac{0}{2} = 0$

This is the DFA

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wat about the below one ... only difference between below one and above one is ..."below one doesnot accept epsilon whereas above one accepts epsilon"

Answer 1

It will be explicitly mentioned in the GATE exam if epsilon have to be included or not. 

In the question asked by you, according to me we dont need to consider the epsilon case as epsilon means "We are not giving anything to machine" If we are not giving anything and (NOT GIVING ANYTHING) divided by 2 is ABSURD....

 (see link below)

http://stackoverflow.com/questions/15330027/regular-expression-for-binary-numbers-divisible-by-3

But according to the below link, 

https://gateoverflow.in/10366/dfa-to-accept-a-binary-number-divisible-by-2

We should consider epsilon.

So i think it will be explicilty mentioned in the exam. :)