Answers on the bottom. Also, you can bring a notecard (5in x 7in max) with notes or whatnot.
True or false? Turing first described a test between a monkey and a human before describing a test between a human and a machine.
True or false? The goal of the machine is to convince the judge that the human is a machine.
True or false? To pass the Turing test, the machine should be expected to fool the judge (convince the judge that the machine is a human) nearly 100% of the time; or, maybe just 70% of the time.
True or false? Dennett thinks that winning a chess championship is just as strong a test for computer intelligence as the Turing test.
Give an initial state, describe possible actions and the transition model (i.e., how states connect), and specify a goal criterion for the following search problem:
A robot wants a path to exit a maze. The maze is represented as a square grid; open areas are represented by white grid cells, and walls are represented by black grid cells.
Repeat this exercise for the following search problem:
Recall from calculus that the derivative is the inverse of the integral. Finding the derivative of a formula is easy (no search needed). But finding the integral of a formula is often challenging, and may require a search procedure. Describe this search procedure.
Complete the following table for weighted (different branches have different costs), finite search graphs:
Search algorithm | Always complete? | Always optimal? | Uses a heuristic? |
---|---|---|---|
Random search | |||
Breadth-first search | Yes | ||
Depth-first search | No | ||
Best-first search | |||
A* search | Yes |
Recall the Goodale route search problem from Practice with searching
notes. Answer the following questions for each of breadth-first
search, depth-first search, best-first search, and A* search (using
some heuristic like distance “as the crow flies”). Assume we start at
Woodruff & Tuttle
and the goal is Goodale parking lot
. For each
question, there may be more than one correct answer.
- What are the first two states (beyond
Woodruff & Tuttle
) that will be checked? - What does the
tocheck
list look like after checking those states from question 1? Be sure to order the list by an appropriate sort order (breadth-first, best-first, and A* will take the next state from the front of the list; depth-first will take the next state from the end).
What is the singular requirement for a heuristic to be called “admissible?”
Describe a utility function for an adversarial search procedure (e.g., minimax) for playing chess.
True or false? Minimax is an appropriate search procedure for single-player games (like a solitaire card game or a Rubik’s cube)?
True or false? Alpha-beta pruning, as applied to the minimax procedure, produces more optimal solutions (e.g., produces game moves that allow the computer to win in fewer moves).
True or false? Alpha-beta pruning (applied to minimax) uses different utility functions than regular minimax.
True or false? Alpha-beta pruning (applied to minimax) is the same algorithm as minimax, just faster because irrelevant computations are omitted.
What is the best move, according to a minimax procedure, for ‘x’ to make in the following tic-tac-toe board?
o | o | x |
x | ||
x | o |
Simplify the following expression using Boole’s and De Morgan’s laws:
Build a truth-table for:
Given,
$(S ∨ T) ∧ (A ∨ B)$ $S → Q$ $¬ Q$ $¬ C ∨ Q$
Prove (and state the rules and premises you utilize):
$¬ S$ $T$ $¬ C ∨ W$
Rewrite the following statements in first-order logic:
- Tony is a tiger.
- All tigers have stripes.
- Some tigers are white.
- If any tiger is white, then we know it lives in the snow (but not necessarily vice versa).
- A tiger is not both white and orange.
Rewrite the following without using
Rewrite the following without using
True or false? Turing first described a test between a monkey and a human before describing a test between a human and a machine.
False — the original test was between a man and a woman; the man was supposed to impersonate the woman.
True or false? The goal of the machine is to convince the judge that the human is a machine.
True — or, False — my fault, both answers are true: the machine is supposed to convince the judge that it is a human, which is equivalent to convincing the judge that the human is a machine.
True or false? To pass the Turing test, the machine should be expected to fool the judge (convince the judge that the machine is a human) nearly 100% of the time; or, maybe just 70% of the time.
False — the machine should not be expected to be “more human than human,” so convincing the judge just 25% of the time seems sufficient. Over 50% may well change our definition of humanity…
True or false? Dennett thinks that winning a chess championship is just as strong a test for computer intelligence as the Turing test.
False — beating humans in chess is not sufficient because chess requires only a narrow kind of intelligence, more calculation than anything
Give an initial state, describe possible actions and the transition model (i.e., how states connect), and specify a goal criterion for the following search problem:
A robot wants a path to exit a maze. The maze is represented as a square grid; open areas are represented by white grid cells, and walls are represented by black grid cells.
- initial state: the robot’s starting location
- possible actions: move north, south, east, west (not all movements are always possible)
- transition model: look at the map, connect grid locations via north/south/east/west links
- goal criterion: finding the exit from the maze
Repeat this exercise for the following search problem:
Recall from calculus that the derivative is the inverse of the integral. Finding the derivative of a formula is easy (no search needed). But finding the integral of a formula is often challenging, and may require a search procedure. Describe this search procedure.
- initial state: the starting formula that needs a symbolic integral to be found
- possible actions / transition model: create a database like this:
sin(x) --> -cos(x)
cx --> cx^2/2
x^n --> (x^(n+1)/(n+1))
- …
- goal criterion: say you are looking at a new formula
g
, and the original formula isf
, then you wantdg/dx = f
; every “state” (formula) is checked in this way
Complete the following table for weighted (different branches have different costs), finite search graphs:
Search algorithm | Always complete? | Always optimal? | Uses a heuristic? |
---|---|---|---|
Random search | Yes | No | No |
Breadth-first search | Yes | No | No |
Depth-first search | Yes | No | No |
Best-first search | Yes | No | Yes |
A* search | Yes | Yes | Yes |
Recall the Goodale route search problem from Practice with searching
notes. Answer the following questions for each of breadth-first
search, depth-first search, hill-climbing search, best-first search,
and A* search (using some heuristic like distance “as the crow
flies”). Assume we start at Woodruff & Tuttle
and the goal is
Goodale parking lot
. For each question, there may be more than one
correct answer.
- What are the first two states (beyond
Woodruff & Tuttle
) that will be checked?- breadth-first (one possible answer):
Lane & Tuttle
,High & Woodruff
- depth-first (one possible answer):
Lane & Tuttle
,SR-315 & Lane
- best-first (only answer):
High & Woodruff
,High & 15th
- A* (only answer):
Lane & Tuttle
,High & Woodruff
- breadth-first (one possible answer):
- What does the
tocheck
list look like after checking those states from question 1? Be sure to order the list by an appropriate sort order (breadth-first, hill-climbing, best-first, and A* will take the next state from the front of the list; depth-first will take the next state from the end). Assume already-checked states are not added.- breadth-first (one possible answer):
[SR-315 & Lane, High & 15th]
- depth-first (one possible answer):
[High & Woodruff, SR-315 I-670 offramp, SR-315 & King]
- best-first:
[High & 11th, US-23 & 15th, Lane & Tuttle]
- A*:
[High & 15th, SR-315 & Lane]
- breadth-first (one possible answer):
What is the singular requirement for a heuristic to be called “admissible?”
- The heuristic must always underestimate (or exactly match) the true cost from the current state to the goal state.
Describe a utility function for an adversarial search procedure (e.g., minimax) for playing chess.
- One possible answer: Number of captured pieces, maybe with a weight for each piece (so a queen will have a large weight, a pawn not so much)
True or false? Minimax is an appropriate search procedure for single-player games (like a solitaire card game or a Rubik’s cube)?
False — there is no adversary to simulate and minimize, thus no minimax
True or false? Alpha-beta pruning, as applied to the minimax procedure, produces more optimal solutions (e.g., produces game moves that allow the computer to win in fewer moves).
False — alpha-beta does not change the solutions.
True or false? Alpha-beta pruning (applied to minimax) uses different utility functions than regular minimax.
False — the utility functions are not changed, just which parts of the search space are actually searched.
True or false? Alpha-beta pruning (applied to minimax) is the same algorithm as minimax, just faster because irrelevant computations are omitted.
True — that’s all alpha-beta pruning is; it still does minimax.
What is the best move, according to a minimax procedure, for ‘x’ to make in the following tic-tac-toe board?
o | o | x |
x | ||
x | o |
The answer is that ‘x’ should move in the exact middle, as proved by this minimax search tree:
Simplify the following expression using Boole’s and De Morgan’s laws:
- Change
$y ∨ ¬ y$ to$T$ , yielding:$¬(¬ x ∨ ¬ y) ∧ (x ∧ T)$ - Change
$x ∧ T$ to$x$ , yielding:$¬(¬ x ∨ ¬ y) ∧ x$ - Distribute the negative, yielding:
$(x ∧ y) ∧ x$ - Get rid of parentheses, reduce redundancy, yielding
$x ∧ y$
Build a truth-table for:
T | T | T | T |
T | F | F | F |
F | T | F | T |
F | F | T | T |
Build a truth table to find this:
T | T | T | T | T | F |
T | T | F | F | F | F |
T | F | T | F | F | F |
T | F | F | F | F | F |
F | T | T | T | T | T |
F | T | F | F | T | T |
F | F | T | F | T | T |
F | F | F | F | T | T |
The last four rows will provide satisfying assignments.
Given,
$(S ∨ T) ∧ (A ∨ B)$ $S → Q$ $¬ Q$ $¬ C ∨ Q$
Prove (and state the rules and premises you utilize):
-
$¬ S$ - From 2, 3 and modus tollens.
-
$T$ - From
$¬ S$ (above) and 1, simplification, and disjunctive syllogism.
- From
-
$¬ C ∨ W$ - From 3, 4 and disjunctive syllogism (which gives us
$¬ C$ ); now apply addition plus introduce the arbitrary symbol$W$ (which is allowed with the addition rule)
- From 3, 4 and disjunctive syllogism (which gives us
Rewrite the following statements in first-order logic:
- Tony is a tiger.
$Tiger(Tony)$
- All tigers have stripes.
$(∀ x)(Tiger(x) → Striped(x))$
- Some tigers are white.
$(∃ x)(Tiger(x) ∧ White(x))$
- If any tiger is white, then we know it lives in the snow (but not
necessarily vice versa).
$(∀ x)((Tiger(x) ∧ White(x)) → LivesInSnow(x))$
- A tiger is not both white and orange.
$(∀ x)(Tiger(x) → (¬ White(x) ∨ ¬ Orange(x)))$
Rewrite the following without using
Rewrite the following without using