Confusion in understanding a DFA question I am new to DFA and I am trying to understand the following question.
The alphabet is Σ = {0, 1}
Construct DFA for L = {0^n: n is either a multiple of 3 or a multiple of 5 }
Question
The above language does not say anything about the 1s.
When we write strings in this Language, we get
L = {є, 000, 00000, 000000, 000000000, ...}
There are no ones in this language.
According to the language description, 0010 would not be a valid string. Right?
So, in the DFA that we construct do we need to show 1s? Can I just leave them out?
Either you can make a 1 transition from every state to a non-final sink state. Or make a note that any character that doesn't match an available transition goes to a non-final sink state.
Depends on what format is usual for the course.
I assume the reason that 1 is also in the alphabet is to trip up people who forget about this sink state.