(* The DFA shown in the homework assignment.  It accepts strings where *)
(* there is an even number of 1's and an even number of 0's.  The first *)
(* input is valid, the second is not. *)
let dfa1 = ("0",
   [("0", "0", "2"); ("0", "1", "1"); ("1", "0", "3"); ("1", "1", "0");
    ("2", "0", "0"); ("2", "1", "3"); ("3", "0", "1"); ("3", "1", "2")],
   ["0"]);;
let dfa1input1 = ["0";"1";"0";"1";"0";"0"];;
let dfa1input2 = ["0";"1";"0";"1";"0";"0";"1"];;

(* This DFA simulates a coffee machine.  The input is a series of *)
(* coins: either a nickel ('n'), dime ('d'), or quarter ('q').  Once *)
(* the input reaches $0.30, the machine will make coffee, and possibly *)
(* return change (although we aren't dealing with the change return). *)
(* The states are numbered as to the amount of money entered so far. *)
(* Of the two inputs after the DFA spec, the first is valid and the *)
(* second is not *)
let dfa2 = ("0",
	    [("0", "n","5" );("0", "d","10");("0" ,"q","25");
	     ("5", "n","10");("5", "d","15");("5", "q","30");
	     ("10","n","15");("10","d","20");("10","q","35");
	     ("15","n","20");("15","d","25");("15","q","40");
	     ("20","n","25");("20","d","30");("20","q","45");
	     ("25","n","30");("25","d","35");("25","q","50")],
	    ["30";"35";"40";"45";"50"]);;
let dfa2input1 = ["n";"d";"n";"q"];;
let dfa2input2 = ["d";"d";"n";"q";"n"];;

(* The NFA shown in the homework assignment.  The first input is *)
(* valid, the second is not.  *)
let nfa1 = ("0",
   [("0", "a", "1"); ("0", "a", "2"); ("1", "a", "1"); ("1", "a", "2");
    ("2", "b", "1"); ("2", "b", "3"); ("3", "a", "1"); ("3", "a", "2")],
   ["0"; "1"]);;
let nfa1input1 = ["a";"b";"a";"b";"a";"b";"a";"a";"a";"b";"a";"a"];;
let nfa1input2 = ["a";"a";"b";"a";"b";"b"];;

(* This NFA will accept strings of the form a+b+ or a+c+.  More *)
(* formally, it accepts strings of the regular expression a+(b+|c+) *)
(* The first input is valid, the second is not.  *)
let nfa2 = ("0",
	    [("0","a","1"); ("0","a","3"); ("1","a","1"); ("1","b","2");
	     ("2","b","2"); ("3","a","3"); ("3","c","4"); ("4","c","4") ],
	    ["2";"4"]);;
let nfa2input1 = ["a";"a";"a";"b"];;
let nfa2input2 = ["a";"a";"a";"b";"b";"b";"b";"c"];;


(* Converts a string into a string list *)
let explode s =
  let c2s = String.make 1 in
  let rec expl i l =
    if i < 0 then l else
    expl (i - 1) ((c2s s.[i]) :: l) in
  expl (String.length s - 1) [];;

(* Thus, you can call your functions this way: *)
(* nfasimulate nfa2 (explode "aaaaabbbbbc");; *)