Written Homework #1

Due Feb 22

1. [30pts, 5 each] Consider the following AI systems. For each, write a short P.E.A.S. (Performance, Environment, Actuators, Sensors) description. For each, characterize the environment [observable, deterministic, episodic, static, discrete, multi-agent].

2. [10 pts] DOGCAT is a simple word game which you may have seen before. The player is given two words with the same number of letters (we will be using 3 letter words) in each. For example, DOG and CAT. He or she has to change the first word into the second (or goal) word by replacing one letter at a time with any other letter as long as the result is a proper English word. For example, we could change DOG to FOG but not to GOG (not a proper English word) or to GOD (two letters were changed). Thus, one way of getting from DOG to CAT might be: DOG => COG => COT => CAT. TO make it more interesting, if you replace a letter with a vowel it costs 2 points, otherwise it costs 1 point. Represent this as a search problem. What will a ``state'' be? What's the initial state, successor function, goal test, path cost?

3. [10 pts] One famous AI problem is to find the possible molecular structures of known constituent atoms that match mass spectroscopic analysis data. This is called the ``structure-elucidation problem''.
This is a big problem in organic chemistry—you can easily find out the constituent atoms (i.e. the chemical formula, such as C6H12O4 but these same 22 atoms can be arranged in many many ways to make different molecules, and the different arrangements matter a great deal. You can write the most important parts of the arranged structure by writing each atom as being connected to one or more of the others above, below, left, or right by a single or double bond (this is a simplification, of course). For example one arrangement of C3O3H3 is:

 H   H
  |    |
  C=O-C-O=C
  |
  O-H

The best information about the arrangement of the atoms is obtained by using a mass spectrometer (and other similar equipment). The mass spectrometer breaks apart the molecule and creates a histogram of particles of various masses. For example, the molecule above might have a mass spectrogram with 2 particles of mass 4, 18 particles of mass 7, 8 particles of mass 10, etc.

 Assume you have a fast mass spectrogram computer simulator, which takes as input a chemical structure file like the ASCII picture above, and returns the mass spectrogram. You also have the subtance's chemical formula and the actual mass spectrogram from the real substance. If the simulated and real mass spec are equivalent, then your ASCII picture is correct. Now, characterize the structure-elucidation problem as a search problem. What will a ``state'' be? What's the start state, goal test, operators, path cost?

HINT: Make SURE you understand what the goal test is for this problem.... The last paragraph is very important. Warning: I gave you more information that you really needed for the answer I am expecting, and certainly not enough info to do this for real.

4. [Undergrads 20 pts / Grads 10 pts] Consider that you have to color a map of Australia with only four colors in such a way that no two adjacent regions have the same color. 

Set up a state space search formulation for this that is precise enough to be implemented:

• [5 / 3 pts] give the state and initial state description as a data structure and constant (in Lisp or whatever language you are using for your programs)
• [7 / 3 pts] define a goal test on states as some test on the data structure
• [8 / 4 pts] define a successor function that takes a state and returns a list of the successor states in your formulation

[Graduate students only, 10 pts] The straightforward solution here generates a tree with 7!(4⁷) leaves, if drawn out completely. Formulate the problem as above so that the complete tree has only 4⁷ leaves.

5. [30 pts, 10 each] After a football game, you are trying to get from South Campus back up to the Laird Campus with your pet golden fox, your pet blue hen, and a bushel of blue corn. The UDel bus rules only allow you to carry one pet with you at a time, and the bus drivers won't allow you to bring anything else with you when you carry that bushel basket of corn. Sad to say, while you love your pets, your fox would, if left to its own devices, devour your blue hen, and your hen would devour your blue corn if possible. Fortunately, you now know several blind search methods to calculate a sequence of steps that will get all four of you across campus undigested.

• Formulate this as a search problem. What are the states, operators, goal test, path costs?
• Of breadth- and depth-first search, which is guaranteed to find a safe plan in the fewest number of bus trips? Assume you do not check whether a node has been previously explored in the tree.
• Trace the search tree produced by the method you named above. (you don't have to expand redundant nodes)