1. As mentioned in class, and described in Section 1.5.10 of Poole & Mackworth text, the dimensions of complexity of an intelligent system interact with one another.

What is a possible interaction between the Learning dimension and the Number of Agents dimension? (Note: There is certainly more than one good answer.)

2. Suppose we are going to hash numbers into a hash table using open addressing with double hashing. Thus there are two auxiliary hash functions, h₁(k) and h₂(k) (where k is the value of the key to be hashed). The successive locations for probes into a hash table of size n are given by the function

h(k,i) = (h₁(k) + i*h₂(k)) % n, for i = 0, 1, 2, , n-1.

Suppose:

n = 19

h₁(k) = k²

h₂(k) = 1 + ( k % 18)

Hash the first eleven prime numbers into this table, in order.

In the table below, show the location into which the each successive number is placed.

I have done the first five for you. Your job is to fill in the tables for the last six. See next page. You just need to show the tables, not your work. You only need to fill in the unshaded rows.

Here are the first 11 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

Hint: I found it easiest to use a spreadsheet to do the calculations.

3.Recall the Winograd schemas we talked about in class, where it takes intelligence to answer the question correctly.

• The city council refused the demonstrators a permit because they feared violence.
  • Who feared violence? (the city council)
• The city council refused the demonstrators a permit because they advocated violence.
  • Who advocated violence? (the demonstrators)

Invent a pair of Winograd schema questions of your own. Look online for ideas, but dont copy them.