I'm being asked to construct a DFA for the language over $\{0,1\}$ such that each string of five consecutive symbols contain at least two zeroes. In my construction, it seems to me that it would make it easier if I could simply lead invalid strings to a "rejection state".
My question is whether such a "rejection state" is accepted convention: I am imagining something like this:
Where $q_3$ is the final, or accepting state, and $\emptyset$ is simply a state that denotes that the DFA rejects the string. Is such a "rejecting state" acceptable to write? Is it conventional? Any other thoughts on the matter?
Best Answer
DFA's don't usually have "reject" states. But you can model these by so-called "sink" states: states which, once entered, you can never leave. What transitions from your $\varnothing$ state can you think of that will turn it into a sink?