1. CPS 001 12.1 Today’s topics l Computability ä Great Ideas Ch. 14 l Artificial Intelligence ä Great Ideas Ch. 15 l Reading up to this point ä Course Pack ä Great Ideas Ch. 1-4,7,11-12

2. CPS 001 12.2 What can be computed l What class of problems can be solved? ä G4, 500Mhz Pentium III, Cray, pencil? ä Alan Turing proved some things, hypothesized others Halting problem, Church-Turing thesis l What class of problems can be solved efficiently? ä Problems with no practical solution what does practical mean? ä Problems for which we can’t find a practical solution solving one solves them all

3. CPS 001 12.3 Schedule students, minimal conflicts l Given student requests, available teachers ä write a program that schedules classes ä Minimize conflicts l Add a GUI too ä Web interface ä … I can’t write this program because I’m too dumb

4. CPS 001 12.4 One better scenario I can’t write this program because it’s provably impossible

5. CPS 001 12.5 Another possible scenario I can’t write this program but neither can all these famous people

6. CPS 001 12.6 Not impossible, but impractical l Towers of Hanoi ä How long to move n disks? l What combination of switches turns the light on? ä Try all combinations, how many are there? ä Is there a better way?

7. CPS 001 12.7 Travelling Salesperson l Visit every city exactly once l Minimize cost of travel or distance l Is there a tour for under $2,000 ? less than 6,000 miles? l Is close good enough? Try all paths, from every starting point -- how long does this take? a, b, c, d, e, f, g b, a, c, d, e, f, g...

8. CPS 001 12.8 Complexity Classifications l This route hits all cities for less than $2,000 --- verify properties of route efficiently. l Hard to find optimal solution Pack trucks with barrels, use minimal # trucks Ideas? Problems are the “same hardness”: solve one efficiently, solve them all

9. CPS 001 12.9 Are hard problems easy? l P = easy problems, NP = “hard” problems ä P means solvable in polynomial time Difference between N, N 2, N 10 ? ä NP means non-deterministic, polynomial time guess a solution and verify it efficiently l Question: P = NP ? ä if yes, a whole class of difficult problems can be solved efficiently---one problem is reducible to another ä if no, none of the hard problems can be solved efficiently ä showing the first problem was in NP was an exercise in intellectual bootstrapping (1971)

10. CPS 001 12.10 Theory and Practice l Number theory: pure mathematics ä How many prime numbers are there? ä How do we factor? ä How do we determine primeness? l Computer Science ä Primality is “easy” ä Factoring is “hard” ä Encryption is possible top secret public-key cryptography randomized primality testing

11. CPS 001 12.11 BRAIN

12. CPS 001 12.12 Imaging the Brain

13. CPS 001 12.13 Some facts… l 100 Billion neurons l On average, connected to 1 K others l Neurons are slow. Firing rates < 100 Hz. l Can be classified into ä Sensory ä Motor ä Central

14. CPS 001 12.14 Sensory Systems l Vision (nearly 30-50% ) l Audition (nearly 10%) l Somatic l Chemical ä Taste ä Olfaction

15. CPS 001 12.15 Motor Systems l Locomotion l Manipulation l Speech

16. CPS 001 12.16 Central Systems l Reasoning and problem solving l Language l ……..

17. CPS 001 12.17 NEURON

18. CPS 001 12.18 Moravec’s argument ä Hans Moravec: ROBOT ä Trends in biological and machine brain evolution l 1 neuron = 1000 instructions/sec l 1 synapse = 1 byte of information l Human brain then processes 10^14 IPS and has 10^14 bytes of storage l In 2000, we have 10^9 IPS and 10^9 bytes on a desktop machine l In 25 years, assuming Moore’s law we obtain human level computing power

19. CPS 001 12.19

20. CPS 001 12.20

21. CPS 001 12.21

22. CPS 001 12.22

23. CPS 001 12.23 Agents and Environments

24. CPS 001 12.24 Reflex agent

25. CPS 001 12.25 Reflex agent with state

26. CPS 001 12.26 Goal-oriented agent

27. CPS 001 12.27 Utility-based agent