Question 1. Figure 1 shows the current layout of a tic-tac-toe game board, and Max (“X”) is going to make the next move. Please draw the remaining states of the game tree, and explain what is the best move for Max.

Question 2. Given a two-player game tree in Figure 2, starting from the root node, please list the nodes in the order they are visited by α-β pruning. Please show the utility values of every node, and report nodes pruned by α-β pruning.

Question 3. Given a two-player game tree in Figure 3, please list correct α value for each Max node, and correct β value for each Min node (no need to report α, β values for nodes pruned by α-β pruning).

Question 4. Figure 4 shows a portion of an imperfect tic-tac-toe game tree using evaluation function. Assume X is the Max player and O is the Min player. Assume a heuristic function is defined as the number of X’s winning position subtract the number of O’s winning position. For example, for board layout , X has 6 winning positions, and O has 5 winning positions. Therefore, the heuristic value of this board layout is 6-5=1.

• Using defined heuristic function, list the heuristic values for all leaf nodes.

• Assume X is the root player, applying α-β pruning to the game tree in Figure 4, determine α value for Max node, and β value for Min nodes.

• Determine nodes which are pruned by α-β pruning, and also specify the best move for X.

Question 5. What is the semantic (meaning) of the following sentence? Show detailed steps to decompose sentence into CNF format.

tictactoealphabeta

tictactoeminmax