Download Artificial Intelligence

Computation
Binary Numbers
• Decimal numbers
• Binary numbers
http://faculty.mc3.edu/pvetere/Applets/APPLETS/NUMSYS/applet_frame.htm
Text
Computers have revolutionized our world. They have
changed the course of our daily lives, the way we do
science, the way we entertain ourselves, the way that
business is conducted, and the way we protect our
security.
Text
Computers have revolutionized our world. They have
changed the course of our daily lives, the way we do
science, the way we entertain ourselves, the way that
business is conducted, and the way we protect our
security.
Les ordinateurs ont révolutionné notre monde. Ils ont
changé le cours de notre vie quotidienne, notre façon de
faire la science, la façon dont nous nous divertissons, la
façon dont les affaires sont menées, et la façon dont
nous protégeons notre sécurité.
Text
Computers have revolutionized our world. They have
changed the course of our daily lives, the way we do
science, the way we entertain ourselves, the way that
business is conducted, and the way we protect our
security.
Les ordinateurs ont révolutionné notre monde. Ils ont
changé le cours de notre vie quotidienne, notre façon de
faire la science, la façon dont nous nous divertissons, la
façon dont les affaires sont menées, et la façon dont
nous protégeons notre sécurité.
計算機已經徹底改變我們的世界。當然，他們已經改變了我
們的日常生活中，我們這樣做科研，我們自娛自樂的方式，
經營的方式進行的方式，以及我們保護我們的安全。
Representing Text
• Decide how many characters we need to represent.
• Determine the required number of bits.
• Ascii: 7 bits. Can encode 27 = 128 different symbols.
Ascii
http://www.krisl.net/cgi-bin/ascbin.pl
Representing Text
F
o
u
r
01000110 01101111 01110101 01110010
Representing Text
T h e
n u m b e r
i s
1 7 .
54 68 65 20 6E 75 6D 62 65 72 20 69 73 20 31 37 2E
When We Need More Characters
What about things like:
简体字
When We Need More Characters
What about things like:
简体字
Answer: Unicode: 32 bits. Over 4 million characters.
http://www.unicode.org/charts/
A conversion applet:
http://www.pinyin.info/tools/converter/chars2uninumbers.html
But What Do Symbols Look Like?
Computers have revolutionized our world.
Computers have revolutionized our world.
Computers have revolutionized our world.
Computers have revolutionized our world.
Computers have revolutionized our world.
The Basic Idea
results = google(text, query)
The Basic Idea
results = google(text, query)
if word_count(text) > 5000:
return(“Done!!”)
else:
return(“No sleep yet.”)
The Basic Idea
results = google(text, query)
if word_count(text) > 5000:
return(“Done!!”)
else:
return(“No sleep yet.”
display = render(text, font)
The Basic Idea
Computers have revolutionized our world.
Digital Images
Pixels
Pixels
Now we must turn this 2-dimensional bit matrix into a string of
bits.
Pixels
0000110000 0001111000 0011111100
0111111110 0111111110 0111111110
0111001110 0111001110 0111001110 0111001110
Digital Images
Two Color Models
RGB
The red channel
RGB
The green channel
RGB
Red
Green
Blue
Experimenting with RGB
http://www.jgiesen.de/ColorTheory/RGBColorApplet/rgbcolorapplet.html
Representing Sounds
Digitizing Sound
Representing Programs
public static TreeMap<String, Integer> create() throws IOException
public static TreeMap<String, Integer> create() throws IOException
{ Integer freq;
String word;
TreeMap<String, Integer> result = new TreeMap<String,
Integer>();
JFileChooser c = new JFileChooser();
int retval = c.showOpenDialog(null);
if (retval == JFileChooser.APPROVE_OPTION)
{ Scanner s = new Scanner( c.getSelectedFile());
while( s.hasNext() )
{ word = s.next().toLowerCase();
freq = result.get(word);
result.put(word, (freq == null ? 1 : freq + 1));
}
}
return result;
}
}
Chess Boards
Forsythe-Edwards Notation
rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
http://en.wikipedia.org/wiki/Forsyth-Edwards_Notation
Molecules
It’s just a string:
AUGACGGAGCUUCGGAGCUAG
The Roots of Modern Technology
1834
Charles Babbage’s
Analytical Engine
Ada writes of the engine, “The
Analytical Engine has no
pretensions whatever to
originate anything. It can do
whatever we know how to
order it to perform.”
The picture is of a model built in the late 1800s by Babbage’s son
from Babbage’s drawings.
Using Logic
•
TaiShanHasTail
•
SmokyHasTail
•
PuffyHasTail
•
ChumpyHasTail
•
SnowflakeHasTail
Using Logic
•
Panda(TaiShan).
•
Bear(Smoky).
•
x (Panda(x)  Bear(x).
•
x (Bear(x)  HasPart(x, Tail)).
•
x (Bear(x)  Animal(x)).
•
x (Animal(x)  Bear(x)).
•
x (Animal(x)  y (Mother-of(y, x))).
•
x ((Animal(x)  Dead(x))  Alive(x)).
Does TaiShan have a tail?
Search
Start state
Goal state
http://www.javaonthebrain.com/java/puzz15/
What is a
Heuristic?
What is a
Heuristic?
The word heuristic comes from
the Greek word 
(heuriskein), meaning “to
discover”, which is also the origin
of eureka, derived from
Archimedes’ reputed
exclamation, heurika (“I have
found”), uttered when he had
discovered that the volume of
water displaced in the bath equals
the volume of whatever (him) got
put in the water. This could be
used as a method for determining
the purity of gold.
What is a
Heuristic?
The word heuristic comes from
the Greek word 
(heuriskein), meaning “to
discover”, which is also the origin
of eureka, derived from
Archimedes’ reputed
exclamation, heurika (“I have
found”), uttered when he had
discovered that the volume of
water displaced in the bath equals
the volume of whatever (him) got
put in the water. This could be
used as a method for determining
the purity of gold.
A heuristic is a rule that
helps us find something.
An Aside on Checking Facts on the Web
Who invented the 15-puzzle?
Sam Loyd did: (http://www.jimloy.com/puzz/15.htm )
Did he or didn’t he:
(http://www.archimedes-lab.org/game_slide15/slide15_puzzle.html )
No he didn’t: (http://www.cut-the-knot.org/pythagoras/fifteen.shtml )
Breadth-First Search
Is this a good idea?
Depth-First Search
More Interesting Problems
The 20 legal initial moves
Scalability
Solving hard problems
requires search in a large
space.
To play master-level
chess requires searching
about 8 ply deep. So
about 358 or 21012 nodes
must be examined.
Growth Rates of Functions
Scalability
To play one master-level
game
21012 nodes
Seconds since Big Bang
3 1017
Number of sequential games 150,000
since Big Bang
Yet This Exists
How?
A Heuristic Function for Chess
c1 * material +
c2 * mobility +
c3 * king safety +
c4 * center control + ...
Computing material:
Pawn
Knight
Bishop
Rook
Queen
King
100
320
325
500
975
32767
The Advent of the Computer
1945 ENIAC The first electronic digital computer
1948 Modified to be a stored program machine
1949 EDVAC
Possibly the first
stored program
computer
Moore’s Law
http://www.intel.com/technology/mooreslaw/
How It Has Happened
Can This Trend Continue?
http://www.nytimes.com/2010/08/31/science/31compute.html?_r=1
How Much Compute Power Might It Take?
http://www.frc.ri.cmu.edu/~hpm/book97/ch3/index.html
How Much Compute Power is There?
Hans Moravec: http://www.frc.ri.cmu.edu/~hpm/talks/revo.slides/power.aug.curve/power.aug.gif
How Much Compute Power Is There?
Kurweil’s Vision
http://www.pocket-lint.co.uk/news/news.phtml/12920/13944/Computersmatch-humans-by-2030.phtml
Some Other People Agree
http://www.networkworld.com/news/2009/092109-intel-cto-interview.html
Countdown to Singularity
Law of Accelerating Returns
Limits to What We Can Compute
Are there fundamentally uncomputable things?
• Does God exist?
• What’s the best way to run a country?
• Does this puzzle have a solution?
What Can We Do?
1.
Can we make all true statements theorems?
2.
Can we decide whether a statement is a theorem?
The Halting Problem
Program, M
input string, w
Does M halt on w?
Yes
No
A Simple Example
read name
if name = “Elaine”
then print “You win!!”
else print “You lose ”
Another Example
read number
set result to 1
set counter to 2
until counter > number do
set result to result * counter
add 1 to counter
print result
Programs Debug Programs
Given an arbitrary program, can it be guaranteed to halt?
read number
set result to 1
set counter to 2
until counter > number do
set result to result * counter
add 1 to counter
Suppose number = 5:
print result
result
number counter
1
5
2
2
5
3
6
5
4
24
5
5
120
5
6
Changing It a Bit
Given an arbitrary program, can it be guaranteed to halt?
read number
set result to 1
set counter to 2
until counter > number do
set number to number * counter
add 1 to counter
Suppose number = 5:
print result
result
number counter
1
5
2
1
10
3
1
30
4
1
120
5
1
600
6
How About this One?
Does this program halt on all inputs?
times3(x: positive integer) =
While x  1 do:
If x is even then x = x/2.
Else x = 3x + 1.
Let’s try it.
The Halting Problem Is Undecidable
Program, M
input string, w
Does M halt on w?
Yes
No
Another Undecidable Problem
The Post Correspondence Problem
A PCP Instance With a Simple Solution
i
X
Y
1
b
aab
2
abb
b
3
aba
a
4
baaa
baba
A PCP Instance With a Simple Solution
i
X
Y
1
b
aab
2
abb
b
3
aba
a
4
baaa
baba
Solution: 3, 4, 1
Another PCP Instance
i
X
Y
1
11
011
2
01
0
3
001
110
Another PCP Instance
i
X
Y
1
11
011
2
01
0
3
001
110
The Post Correspondence Problem
List 1
1
2
3
ba
abb
bab
List 2
bab
bb
abb
A PCP Instance With No Simple Solution
i
X
Y
1
1101
1
2
0110
11
3
1
110
A PCP Instance With No Simple Solution
i
X
Y
1
1101
1
2
0110
11
3
1
110
Shortest solution has length 252.
Can A Program Do This?
Can we write a program to answer the following
question:
Given a PCP instance P, decide whether or
not P has a solution. Return:
True if it does.
False if it does not.
What is a Program?
What is a Program?
A procedure that can be performed by a computer.
The Post Correspondence Problem
A program to solve this problem:
Until a solution or a dead end is found do:
If dead end, halt and report no.
Generate the next candidate solution.
Test it. If it is a solution, halt and report yes.
So, if there are say 4 rows in the table, we’ll try:
1
2
3
4
1,1
1,2
1,3
1,4
2,1 ……
1,1,1 ….
1,5
Will This Work?
• If there is a solution:
• If there is no solution:
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
A Tiling Problem
Try This One
Another Tiling Problem
Another Tiling Problem
Is the Tiling Problem Decidable?
Wang’s conjecture: If a given set of tiles can be used to tile an
arbitrary surface, then it can always do so periodically. In other
words, there must exist a finite area that can be tiled and then
repeated infinitely often to cover any desired surface.
But Wang’s conjecture is false.
Important Issues
• The halting problem is undecidable.
• There’s no black box reasoning engine for standard logic.
• Would quantum computing change the picture?
• Does undecidability doom our attempt to make artificial
copies of ourselves?
Is Decidability Enough?
The Traveling Salesman Problem
15
25
10
28
20
4
8
40
9
7
3
23
Given n cities and the distances between each pair of
them, find the shortest tour that returns to its starting point
and visits each other city exactly once along the way.
The Traveling Salesman Problem
15
25
10
28
20
4
8
40
9
7
3
23
Given n cities:
Choose a first city
Choose a second
Choose a third
…
n
n-1
n-2
n!
The Traveling Salesman Problem
Can we do better than n!
● First
city doesn’t matter.
● Order doesn’t matter.
So we get (n-1!)/2.
The Growth Rate of n!
2
2
11
479001600
3
6
12
6227020800
4
24
13
87178291200
5
120
14
1307674368000
6
720
15
20922789888000
7
5040
16
355687428096000
8
40320
17
6402373705728000
9
362880
18
121645100408832000
10
3628800
19
2432902008176640000
11
39916800
36
3.61041
Growth Rates of Functions, Again
Putting it into Perspective
Speed of light
Width of a proton
At one operation in the
time it takes light to
cross a proton
Since Big Bang
Ops since Big Bang
Neurons in brain
Parallel ops since Big
Bang
3108 m/sec
10-15 m
31023 ops/sec
31017 sec
91040 ops
1011
91051
36! = 3.61041
43! = 61052
Does Complexity Doom AI?