Here we show that the A_DFA problem is decidable, and introduce "high-level descriptions" of problems. The idea is to simulate the DFA by keeping track of the current input character as well as the current state, then repeatedly look in the transition function for what state to go next. Then, update that current state; at the end, we look to see if this state is a final state, and accept if and only if it is. The language is then decidable because this Turing Machine runs in a finite amount of time.
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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
