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?