1 (optional; due September 3). Try to improve on the definition of `intelligence' that I offered in class.
2 (due September 10). Modify the model-based reflex vacuum cleaner agent in /home/stone/courses/artificial-intelligence/aima/chapter-2/reflex-agent-with-state.ss so that it keeps track of how many percepts it has received since cleaning each room and moves into any room that has not been cleaned for at least ten percepts.
3 (optional; due September 10). Prove that the model-based reflex vacuum cleaner always finds a condition that matches its internal model of the world, no matter what happens to it.
4 (optional; due September 10). Implement, in Scheme, a performance-measuring environment simulator for the vacuum-cleaner world. Use it to test the vacuum-cleaner agents described in class.
5 (required; due September 17). Use CVS to check out a copy of the ``testing'' project from the repository at cvs.cs.grinnell.edu:/cvs, edit your copy to include an appropriate response after your name, and commit your change back to the CVS repository.
6 (required; due September 22). Use the eight-puzzle solver in /home/stone/courses/artificial-intelligence/aima/chapter-3/eight-puzzle.ss to solve the puzzle by breadth-first search, never expanding any node containing a previously encountered state.
7 (required; due November 3). Use resolution to determine whether the following inference is valid:
Everyone who plays basketball is taller than anyone who drives a Volkswagen Beetle.
No one can be taller than himself.
All of Jerry's friends play basketball.
Therefore, there exists someone who, if he drives a Volkswagen Beetle, is not a friend of Jerry's.
8 (optional; due November 17). In human beings, a sex-linked trait is one that is controlled (or at least influenced) by genes carried on the X chromosome. A female has two X chromosomes, one from each parent; a male has only one, inherited from his mother. A male exhibits such a trait if, and only if, his X chromosome carries the gene that causes it to be expressed. If the trait is recessive, however, a female exhibits the trait only if both of her X chromosomes carry such a gene; if only one does, her children may possibly exhibit the trait, but she herself does not.
Chromosomes and the genes that they carry are normally transmitted unchanged from parents to children. Each child receives one of its mother's X chromosomes, with equal probability; a father transmits his X chromosome to all of his daughters and none of his sons.
Suppose that a trait is exhibited by one in four males and one in sixteen females. What is the prior probability that a female who does not exhibit the trait nevertheless carries a gene for it? (You may assume that the trait has no effect, positive or negative, on reproductive success.) What is the conditional probability that she carries such a gene, given that she has a brother who exhibits the trait?
(Note: I originally stated this problem incorrectly, making the premises internally inconsistent. I restated it on November 18 to remove the inconsistency. My apologies to anyone who found the original version frustrating to work on.)
9 (required; due November 24). Consider a Markov decision process set in the wumpus world of Figure 7.2 of our textbook. Each state has five components: the agent's location, the direction in which it is facing, whether it is holding the gold, whether it still has the arrow, and whether the wumpus is still alive. A state is terminal just in case the agent is holding the gold, or in one of the pits in locations (1, 3), (3, 3), and (4, 4), or in the wumpus's den at (3, 1) while the wumpus is alive. The reward value of a terminal state is the sum of three conditional bonuses: +1000 for holding the gold, -1000 for being in a pit or in the wumpus's den while the wumpus is alive, and -10 for not having the arrow. Every non-terminal state has a reward value of -1.
Initially, the agent is in location (1, 1), is facing right, is not holding the gold, and still has the arrow, and the wumpus is still alive. At each step, the agent can move forward, turn left, turn right, grab, or shoot. These actions have the following effects on the state:
(a) Calculate the expected utility of the sequence [move forward, turn left, move forward, move forward, grab].
(b) Use modified policy iteration to find the agent's optimal policy for addressing this problem.
This document is available on the World Wide Web as
http://www.cs.grinnell.edu/~stone/courses/artificial-intelligence/exercises.xhtml
created August 28, 2003
last revised November 18, 2003