CIS603 S03: Solutions for Homework 1

1. Exercises 1.11, 1.12, and 1.13, pg. 31 Russell and Norvig, 2nd Edition (RN)

The arguments depend on the definition of intelligent and tell. We can take it to an extreme and say: neither computers not animals can be intelligent---they can only do what the laws of physics and chemistry tells their atoms to do. Whatever your argument is, the key is to be consistent with the definition of intelligent and tell for the two exercises. If you assume something about computers, you have to carry that same assumption to animals. Unless your reason for deciding that something is intelligent takes into account the mechanism (programming via genes vs. programming via a human programmer.

There are many different ways of answering this. You can take it to an extrme and argue that neither computers nor animals can be intelligent--- they can only do what the laws of physics and chemistry tell their atoms to do.

2. Problem 3.7, pg. 90, RN

1. Initial state: looking at the first page of the book
   Goal Test: looking at the entry listing Mr. Jimwill Zollicoffer in Alameda
   Operators: look at new book; look at new page; look at new entry on page
   Path costs: measure this in seconds: say 10 for a new book, 2 for a new page, and 0.5 for a new entry.
2. Initial state: looking at the first page of the book
   Goal Test: find someone with the first name Jimwill (or first initial J.)
   Operators: look at new book; look at new page; look at new entry on page
   Path costs: measure this in seconds: say 10 for a new book, 2 for a new page, and 0.5 for a new entry.
   Note that the search strategy is very different when you know the last name, but the formulation as a search problem is similar.
3. Initial state: you are somewhere in the Amazon jungle
   Goal Test: you are at the sea
   Operators: follow stream upstream for a bit; follow stream downstream for a bit, go inland in any direction for a bit
   Path costs: distance travelled
4. Initial state: no regions colored
   Goal Test: all regions colored
   Operators: assign a color to a region
   Path costs: number of assignments
5. Initial state: as described in the book
   Goal Test: monkey has banana
   Operators: hop on crate; hop off crate; push crate from one spot to another; walk from one spot to another; grab banana
   Path costs: number of locations
6. Initial state: you are at some location in town
   Goal Test: you are at the drug store
   Operators: walk forwafd a bit; turn left; turn right; look for drug store sign; ask where drug store is
   Path costs: number of steps

3. Problem 3.17, pg. 93, RN

1. No. The algorithms must still explore every branch because any branch must lead to a sequence of negative-cost transitions or a negative-cost loop.
2. If there is a loop with net negative cost, a rational agent would enter that loop and never leave it---thus generating an infinite reward. The only reason not to enter the loop is if there is a loop with a better reward elsewhere.
3. Humans don't get stuck in loops like this because following the loop never leaves you in the exact state as before you entered. After the first few times, even the most beautiful sceneries become routine, and thus provide less reward. An accurate model of the domain should include the effects on the mental state of the agent. Also, all actions take time and time is part os the state so following a loop leads to a different state.
4. Some psychiatric disorders and various forms of addiction result in looping behavior.

4. Answer the following questions:

1. Give an example of a problem where hill climbing and best first search behave differently. Let T be a tree with two paths: T --> T1 --> T11 -->T111 and T -- > T2 --> T22 where both T111 and T22 are goals. If T22 is optimal, T1 has a better heiristic value than T2, but T2 is better than T11, then hill climbing will choose T111 while best first will choose T22.
2. Construct a finite search tree for which it is possible that depth-first search uses more memory than breadth-first search. Please highlight the goal nodes in your tree. If the tree has a branching factor of 2 and the goal is on the second level, the right-most node, depth-first explores completely the left subtree and requires max-depth nodes, while breadth-first only requires 3 nodes.
3. Construct a problem and a formulation for it so that hill climbing is at least as good as breadth-first search, depth-first search, and best-first search. For example, if you have a tree with a branching factor of 1.
4. Describe a search space where depth-first iterative deepening performs much worse than depth-first search. How many nodes does each algorithm expand? Suppose the goal is the right-most node on the last level in the tree. Depth first expands b^d nodes. Depth first iterative deepening expands b^d + 2 b^{d-1} + 3 b^{d-2} + ... + (d+1) b^0 nodes.

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