Prove that the tic-tac-toe strategy of Example 12.19 is optimal (wins against an imperfect opponent whenever possible, draws otherwise), or give a counterexample. Starting with the tic-tac-toe program...

Prove that the tic-tac-toe strategy of Example 12.19 is optimal (wins against an imperfect opponent whenever possible, draws otherwise), or give a counterexample. Starting with the tic-tac-toe program of Figure 12.4, draw a directed acyclic graph in which every clause is a node and an arc from A to B indicates that it is important, either for correctness or efficiency, that A come before B in the program. (Do not draw any other arcs.) Any topological sort of your graph should constitute an equally efficient version of the program. (Is the existing program one of them?)