The test is open-everything with the sole limitation that you neither solicit nor give help while the exam is in progress.

1. Categorize a shopping bot for an offline bookstore according to each of the six dimensions from Russell and Norvig (fully/partially observable, deterministic/stochastic, episodic/sequential, static/dynamic, discrete/continuous, single/multi agent)
2. Suppose the vacuum cleaner world was extended to have four squares in a walled-in 2 x 2 grid, and two new actions up and down. Suppose also the performance measure was +5 for cleaning a square, -4 for sucking in a clean square, -2 for making a move. A clean square will become dirty if the vacuum enters it for the nth time where n mod 4 = 0. The vacuum can only sense whether the current square it is in is dirty or clean, but it cannot sense its current location. It can attempt a move action and receive a bump percept if the move runs in to an outer wall. Bumping into a wall will leave the agent in the same square, but does not increase the number of times the square is considered entered.
   1. Ignoring belief states, how many states are there in a problem formulation of this world?
   2. Give an agent program for this world that would make this agent rational. Use pseudocode, but be fairly precise. Be sure to describe the model the agent constructs. It may be helpful to sketch (a portion of) the belief state graph.
3. What is the fewest possible number of nodes, in terms of b, d, and m, that will be generated for each of the following? Assume that all nodes have exactly b children. If the strategy can have both goal-test-at-generation-time and goal-test-at-expansion variants, answer for both.
   1. depth-first search with backtracking
   2. depth-first expansion
   3. breadth-first
   4. depth-first iterative deepening
4. Recall that for the A* algorithm, the evaluation function, f, for a node n is such that f(n) = g(n) + h(n) where h(n) is a non-overestimating estimate of the cost to reach a goal from n. What interesting things can you say about the behavior of the algorithm when
   1. h is a perfect estimate
   2. h(n) is zero for every n
5. Extra Credit: Give an example of a road navigation problem for which uniform cost search fails if an algorithm does the goal check on node generation as opposed to goal expansion.