Write a purely functional Scheme function that returns a list of all permutations of a given list. For example, given (a b c), it should return ((a b c) (b a c) (b c a) (a c b) (c a b) (c b a)) (in...

Write a purely functional Scheme function that returns a list of all permutations of a given list. For example, given (a b c), it should return ((a b c) (b a c) (b c a) (a c b) (c a b) (c b a)) (in some order). Modify the Scheme program of Figure 11.1 or the OCaml program of Figure 11.3 to simulate an NFA (nondeterministic finite automaton), rather than a DFA. (The distinction between these automata is described in Section 2.2.1.) Since you cannot “guess” correctly in the face of a multivalued transition function, you will need either to use explicitly coded backtracking to search for an accepting series of moves (if there is one), or keep track of all possible states that the machine could be in at a given point in time.