# NFA: If alphabet {0,1} is given, are you allowed to build a NFA with only 0?

Let's say there is the alphabet {0,1} given and you are supposed to build a NFA for language L= {w | w includes two successive zeroes}.

So we are supposed to build a NFA for the language which only accepts words with two (or more) successive zeroes, where alphabet is {0,1}.

Now my question, is it allowed to build a NFA which only includes zeroes and no 1's?

• What do you mean when you say an NFA "includes" zeroes, and not ones? Since the alphabet is $\{0, 1\}$ you do have to define behavior for when an $1$ is encountered in the input. For example $100$ is in the language, but contains an $1$. – orlp Oct 28 '17 at 15:27
• It's allowed to build an NFA that only has transitions for input $0$s. But are you sure that's what you want? There are strings that contain two or more successive zeroes but also contain $1$s. – David Richerby Oct 28 '17 at 17:03