EECS 492 Midterm #1. Example Questions. Note: Not a complete exam!

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1 EECS 492 Midterm #1 Example Questions Note: Not a complete exam! General Instructions This exam is closed book, except that you are allowed to refer to a single sheet of paper. You may use a calculator if you wish. Write your answers in the space provided, using the backs or attaching extra sheets if needed. Make sure you write your name at the top of every page, and keep your answers on the same page as the question appears. This course operates under the rules of the College of Engineering Honor Code. Sign the pledge below: I have neither given nor received aid on this examination, nor am I aware of any violations of the honor code. signed You have 90 minutes. There are questions, worth a total of 100 points. This exam is worth 12% of your total grade for the course. Be careful to pace yourself; a pace of one point per minute will be a little too slow, and we would recommend that you try to maintain a faster pace than that to give yourself some cushion for checking over your answers at the end. Be utility-based! (Don t spend more time on a question than it is worth, unless you ve finished the other questions.) 1 2 total

2 Problem 1: Short Answer Questions (25 points) A. Fill in the blanks (5 points) : Note: Each blank space should correspond to exactly ONE word. a) If an agent ought to prefer one state of the world S to another state state of the world S', then in AI terminology S is said to have higher for the agent. (Do not use words such as `worth' or `value'; we are looking for a precise technical term.) b) The names of three common difficulties that hill climbing algorithms are susceptible to are: (i) local maxima, (ii) and (iii). c) Although the inner loop of a simulated annealing (SA) algorithm is very similar to hill-climbing (HC), the difference is that while HC always picks the move, SA can sometimes pick a move. B. (10 points) Consider a crossword-puzzle-solving agent, C. The goal of the agent C is to successfully solve the entire crossword puzzle. The goal state, thus, is the fully solved puzzle. Intermediate states are partially solved puzzles. The definition of an operator is as follows: an operator adds one single letter to a non-black square in the puzzle; if the square was empty, then the letter that was added now appears in it as a result of the operator. If the square already had a previous letter in it, that previous letter is overwritten by the new letter that was added. (10 points total) 1) (4 points) Think of the agent C as a utility-based agent. In ONE SENTENCE, state what would be a good utility function for this agent.

3 2) ( points) Suppose that C searches for the goal using a hill-climbing algorithm. What would be the function that C should be trying to maximize? ) ( points) Suppose that the hill-climbing algorithm used by C does not make use of random restarts. Under what circumstances will C run into the local maxima problem? Explain. ( points)

4 Problem 2: First-Order Logic (40pts) In this problem, we will consider a very simplified version of the Towers of Hanoi (TOH) problem. This version is simple in several respects, one of which is that we will only consider 2 disks. The initial situation can be represented as in the picture below. Assume in this case that disk D1 is above disk D2, and they are both on peg P1, which is next to peg P2, which is next to peg P. A. (5 points) The knowledge about this domain and this particular problem are captured in the following axioms, which we have already converted for you into CNF. Under each converted sentence, write in English what the sentence means. We ve already done a few of these for you. 1. Cl(D1, S). (D1 is initially clear. ) 2. On(D1,P1,S). (D1 is initially on P1. ). On(D2,P1,S). ( ) 4. ~Cl(d4,s4) OR ~On(d4,p4a,s4) OR On(d4,p4b,m(d4,p4a,p4b,s4)) (If a disk is clear and on a peg, it will be on some peg in the situation that arises after the disk has been moved from one peg to the other.) 5. ~On(d5a,p5a,s5) OR ~On(d5b,p5a,s5) OR ~On(d5a,p5b,m(d5a,p5a,p5b,s5) OR Cl(d5b,m(d5a,p5a,p5b,s5)) ( ) 6. ~On(d5a,p5a,s5) OR ~On(d5b,p5a,s5) OR ~On(d5a,p5b,m(d5a,p5a,p5b,s5) OR On(d5b,p5a,m(d5a,p5a,p5b,s5)) ( )

5 B. (4 points) We want to use these logic axioms to find a plan to get disk D2 onto peg P. To do this we add the following axiom. Why? 10. ~On(D2, P, sf) OR Ans(sf) D. (20 points) Given axioms 1-6, along with 10, we will use resolution to solve the problem. In your work, be sure to clearly identify which statements are being resolved along with other information such as which substitutions are required for unification. The whole process requires somewhere around 1 resolution steps, about half of which are trivial. However, getting all the way to the end is only worth 1 point; all the rest of the points can be received just by showing your mastery of resolution to get to where the answer variable sf has been replaced by exactly 2 nested actions of moving D2 to P after moving D1. (This took me only 4 resolution steps.) G. (4 points) To ensure that a larger disk isn t placed on a smaller disk, assume that we have a relation LT(disk1,disk2) that says that disk1 is larger than disk2, and axioms to this effect are added to the KB so that this relation is defined between all pairs of disks. Translate the following sentence into first order logic: A disk can be moved from a peg to a different peg if the disk is clear and initially on a peg, unless the peg to which it is to be moved already has a disk on it that is smaller than the disk that was to be moved there.

6 Problem : Search (5 points) B) (6 points 2 points each) 1) What is the basic property of a heuristic that assures us that it is admissible? ) A* with h=0 is the same as what other search algorithm? Be as specific as possible. C) (20 points) The following state space has states labeled with letters, possible successors notated with links, and path-cost between states represented by the numbers on the links. "A" is the start state and "G" is the goal state. (Assume that successors are generated from left to right (e.g., C before B, D before H.) 4 A 2 C E B 2 D 4 H The following table is a list of h-values given by a heuristic for the above nodes: A: 4 B: 5 C: 2 D: E: 1 F: 0 G: 0 H: G F

7 2) (7 points) Apply the A* algorithm to the above problem and show us the final tree. Do not avoid cycling or visiting repeated states. Be sure to show the queue at each step of the algorithm as well as which node is being expanded. In the case of ties of f- cost, do FIFO. What is the optimal path found by A*? ) (10 points) Apply the IDA* algorithm to the above problem. You only need to show us the queue and expansions (though you can draw the tree(s) if you want to). Do not avoid cycling or visiting repeated states. Be sure to show the queue at each step of the algorithm as well as which node is being expanded for each iteration. Also be sure to show when a boundary or future boundary is being chosen. In the case of ties of f-cost, do FIFO. What is the optimal path found by IDA*?