Post on 18-Jan-2016
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
• 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
Example: Towers of Hanoi
Simonas Šaltenis, Aalborg University, simas@cs.auc.dk
1 2 3
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?
Towers of Hanoi
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, simas@cs.auc.dk
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, simas@cs.auc.dk
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?