Written Exercises W2
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Fall 2011
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Numbers in brackets indicate approximate number of points each problem is worth. See the course home page for information on when and where to submit written exercises, and grading criteria. As always, please be very careful to do the right problems for your edition of R&N. A scanned copy of the exercises in R&N (3rd ed.) are available on e-reserves (log on to the COS402 site on blackboard, then click on "e-reserves").
1. [15] Exercise 6.1 in R&N (2nd ed.) OR Exercise 5.9 in R&N (3rd ed.). Assume player X goes first. In part (a), "game" should be interpreted to refer to a complete path through the search tree from the root to a leaf, in other words, a sequence of plays culminating in either a victory for one of the players or a draw. Note that part (a) asks for an approximate estimate, so don't spend a lot of time trying to get an exact answer. In part (e), "optimal order" means that the best successors (in terms of their value) are always examined first.
2. [10] Exercise 6.2 in R&N (2nd ed.) OR Exercise 5.7 in R&N (3rd ed.).
3. [10] Exercise 7.4a,c in R&N (2nd ed.) OR Exercise 7.5a,c in R&N (3rd ed.). Be sure to prove these assertions; don't just "wave your hands".
4. [15] (Adapted from a similar exercise in R&N.) Consider the following facts:
"If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned."
5. [optional -- 5 hops (honors optional points)] This optional exercise asks you to prove the correctness of alpha-beta search. See this pdf for details.