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CS v. 165A Artificial Intelligence, Winter 2011 Assignment #2 Problem Solving and Search Due Tuesday, February 01 before the class
Notes:
Be sure to re-read the Policy on Academic Integrity on the course syllabus. Any updates or corrections will be posted on the Announcements page (home page for the course), so check there occasionally. Hand in your copy in the class (please use word processing editor). Important: Keep your answers precise. Avoid writing a monograph! A few sentences are plenty for each part of your answer.
Problem #1 [30 points] Problem 3.6 in the textbook: 3.6 Give a complete problem formulation for each of the following. Choose a formulation that is precise enough to be implemented. a. Using only four colors, you have to color a planar map in such a way that no two adjacent regions have the same color. b. A 3-foot-tall monkey is in a room where some bananas are suspended from the 8-foot ceiling. He would like to get the bananas. The room contains two stackable, movable, climbable 3-foot-high crates. c. You have a program that outputs the message illegal input record when fed a certain file of input records. You know that processing of each record is independent of the other records. You want to discover what record is illegal. d. You have three jugs, measuring 12 gallons, 8 gallons, and 3 gallons, and a water faucet. You can fill the jugs up or empty them out from one to another or onto the ground. You need to measure out exactly one gallon. Problem #2 [40 points] Problem 3.8 in the textbook:
3.8 In the textbook, we said that we would not consider problems with negative path costs. In this exercise, we this explore decision in more depth. a. Suppose that actions can have arbitrarily large negative costs; explain why this possibility would force any optimal algorithm to explore the entire state space. b. Does it help if we insist that step costs must be greater than or equal to some negative constant c? Consider both trees and graphs. c. Suppose that a set of actions forms a loop in the state space such that executing the set in some order results in no net change to the state. If all of these actions have negative cost, what does this imply about the optimal behavior for an agent in such an environment? d. One can easily imagine actions with high negative cost, even in domains such as route finding. For example, some stretches of the road might have such beautiful scenery as to far outweigh the normal costs in terms of time and fuel. Explain, in precise terms, within the context of state-space search, why humans do not drive around scenic loops indefinitely, and explain how to define the state space and actions for route finding so that artificial agents can also avoid looping. e. Can you think of a real domain in which step costs are such as to cause looping? Problem #3 [10 points] Problem 3.23 in the textbook: 3.23 Trace the operation of A* search applied to the problem of getting to Bucharest from Lugoj using the straight-line distance heuristic. That is, show the sequence of nodes that the algorithm will consider and the f, g, and h score for each node. Problem #4 [20 points] Problem 3.29 in the textbook: 3.29 Prove that if a heuristic is consistent, it must be admissible. Construct an admissible heuristic that is not consistent.