Suppose a particular FA, called FIN, has the property that it had only one final state that was not the start state. During the night, vandals come and switch the + sign with the - sign and reverse the direction of all the edges.
(i) Show that the picture that results might not actually be an FA at all by giving an example.
(ii) Suppose, however, that in a particular case what resulted was, in fact, a perfectly good FA. Let us call it NIF. Give an example of one such machine.
(iii) What is the relationship between the language accepted by FIN and the language accepted by NIF as described in part (ii)? Why?
(iv) One of the vandals told me that if in FIN the plus state and the minus state were the same state, then the language accepted by the machine could contain only palindromic words. Defeat this vandal by example.