Transcript Lecture 39 What Can`t Be Computed?

Lecture # 39
What Can’t Be Computed?
Computability
• Tractable problems (P): Can be solved by a
a computer is some deterministic
(reasonable) polynomial time
– What is a ”reasonable” running time?
• Intractable problems (NP):
1. Guess the solution
2. Answer must be verifiable in polynomial time
Example: Towers of Hanoi
• Goal: transfer all n disks from peg 1 to peg 3
• Rules:
– move one disk at a time
– never place a larger disk on top of a smaller one
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Simonas Šaltenis, Aalborg University, [email protected]
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Towers of Hanoi
How Long?
(http://www.mathcs.org/java/programs/Hanoi/index.html)
Towers of Hanoi
How Long?
• 64 disks
• Move 1 disk per second
• 585 billion years
• Is that tractable/reasonable?
What are some other
hard problems?
Traveling Salesman Problem
• A traveling salesperson needs to visit n cities
• Is there a route of at most d length? (decision problem)
Simonas Šaltenis, Aalborg University, [email protected]
TSP Algorithms
• Naive solutions take n! time in worst-case, where
n is the number of ”legs” or ”hops” on the trip
• No polynomial-time algorithms are known
– TSP is an NP-complete problem
• Longest Path between cities A and B is also
NP-complete
Simonas Šaltenis, Aalborg University, [email protected]
Can Computers Think?
• What is thinking?
(http://www.youtube.com/watch?v=VSdxqIBfEAw)
• How can you measure thinking?
• Does it involve cognition?
• How do you measure/evaluate intelligence?
One Measure of Thinking
• Type a question on a computer
- send a copy to a human
- send a copy to computer
• If, after a reasonable amount of time you
can’t tell which is which, does that mean the
computer is thinking (is intelligent?)
Can Computers Express Emotion?
• Which is harder?
• Thinking
or
• Expressing Emotion?
Can Computers Play Chess?
• What constitutes playing chess?
• How about beating a grand master?
• How can a computer do this without being
able to think?
Can Computers Play Chess?
• Use a big table of possible moves given a
specific board configuration
• Look ahead as far as possible
• Use a database of opening and end games
Can Computers Play Chess?
• Kasparov won IBM’s “DEEP BLUE” in ‘96
• DEEP BLUE beat Kasparov in ‘97
Can Computers be Creative?
• Can computers do art work?
(http://www.soban-art.com/)
• Can computers write stories, compose music?
• Can computers perform medical diagnoses?
• What is Artificial Intelligence?
Can Computers be Creative?
• What is the essence of creativity?
• Is it following procedures or rules?
• Is it unpredictable departure from rules?
• What is the role of agency in creativity?
Can Computers be Creative?
• Is creativity random?
• Is creativity entropic?
• Is creativity algorithmic?