# What is the difference between these 2 dfas for binary strings ending with 00? The first one is from unreputed youtuber whereas second one is from reputed university called adiuni course of theory of computation.

Now I know what that second figure means, it means it also accepts $$\in$$ as initial state=final state, but

1. how I don't know that. This dfa should accept all binary divisble by 4. But how is nothing(it is not zero mind that) divisible by 4?

2. Why I don't know that. I am making a dfa for binary numbers divisible by 4 and adiuni professor told that binary numbers that end with 00 are divisble by 4. So I googled about dfa ending with 00 and got this. I am personally more comfortable at first figure as it is more inituitive to me.

How is $$\in$$ divisible by 4? What does that even mean?

• nothing [is not zero] (reminds me of difficulties ancient Greek philosophers are assumed to have had.) How do you know, how would I without access to the definitions (here: binary) to use? Nov 4, 2021 at 7:35
• I would be inclined to agree with you, I don't know what divisibility even means for the empty string. Nov 6, 2021 at 23:59