Things to remember:
      In the instructor's paradigm, symmetry and abstraction
      are exploited before search.

       Diversity corresponds exactly with Computer Science's
	"worst case complexity".

         Expanding a node means finding its children.

         OPEN means a node is reached but not expanded.
	 CLOSED means a node is not expanded.

	    Search algorithms (most results are in previous posting)
	       I = initial state
	       g =
	       h(S) = estimate of distance h is to the goal
	       g^(S) = shortest path  found so far from initial state to
	        a goal.
               h*(S) = true distance S is from the goal

               f*(S) = length of optimal path through (S).
               f*(I) = length of the optimal solution.



          results:
	      A*-admissible => 
 finds an optimal solution if a
	      solution exists.

              h monotone => h admissible.

              A*-monotone never has to take a node from CLOSED and
	      return to OPEN (hence algorithm can be streamlined).

           Lemma:
	      On each iteration OPEN always has a node from
	       each optimal path to the goal.