[Solved]: Why isn't converting from an NFA to a DFA working?

Problem Detail: 

I am just beginning to learn computation theory. I wrote up a non-deterministic finite automata that accepts strings that contain the substring "abba":

I tried to convert it to a DFA by putting together sets of states in the NFA to be states of the DFA:

However, I just realized that my DFA doesn't accept strings such as "abbaa" that do not end in "abba." That means that my methodology was wrong. Why? I thought it would make sense to combine states of the NFA to make states of the DFA.

Asked By : John Hoffman

Answered By : Luke Mathieson

Your methodology for creating the DFA from the NFA is fine. The problem is that you started with the wrong NFA (you'll notice that your NFA doesn't accept abbaa either). Try this one instead:

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/4572