For people who are wondering, a good argument for showing that a Turing Machine that simulates a DFA on a string ALWAYS halts would be: We know what the string is finite (so it doesn't go on forever). If the DFA given is a proper DFA, in other words, the machine won't brake with any string over the alphabet given, we know that at some point the TM simulating the DFA will stop at some state in the DFA (as string is finite). Hence the state may be an accept state or not => it always either accept or reject a string over the alphabet of the DFA.
Not sure how good this explanation is for the students that learning TM "decidability" for the first time but this is a VERY GOOD review before my Theory of Computation final. THANK YOU !
A bit confused... every context free language is decidable, but you say only some questions about context free languages are decidable but others are not?