1. Alan Turing WWII code-breaker mathematical proof of ‘Turing machines’ …in particular, “Universal Turing machine” laid foundations of computer science father of artificial intelligence

2. Parts of a Turing machine  1. the ‘tape’  stores symbols  divided into ‘squares’  2. the read/write head (i.e. ‘machine head’)  can read/write symbols on tape  3. finite set of internal states q 0,…,q n  4. finite alphabet of symbols b 1,…,b m  5. Machine table (instructions for machine)

3. Basic example: add-two-numbers machine ####11111+ q0q0  alphabet of symbols: “#” = scratch symbol “1” = tally mark “+” = addition symbol  internal states of machine: q 0 q 1  tape:   read-write head: 

4. Basic example: add-two-numbers machine ####11111+ ####1111#1 q0q0 q1q1

5. ####11111+ ####1111#1 q0q0 q1q1 input state

6. Basic example: add-two-numbers machine ####11111+ ####1111#1 q0q0 q1q1 output state

7. Machine table for addition machine: q0q0 q1q1 11, R, q 0 #, Halt +1, R, q 0 ##, L, q 1 symbol read from current tape-square symbol read from current tape-square current internal state

8. Basic example: add-two-numbers machine ####11111+ q0q0

9. ####11111+ q0q0

10. ####11111+ q0q0

11. ####11111+ q0q0

12. ####111111 q0q0

13. ####111111 q0q0

14. ####111111 q0q0

15. ####111111 q0q0

16. ####1111#1 q1q1

17. Physical realizations of Turing machines  we just described ‘parts’ of Turing machines. but these ‘parts’ were abstract specifications. not physical, nuts-and-bolts machines  To realize (or implement) a Turing machine, we need to build a physical system that satisfies the formal description of the machine. 1. symbols given concrete embodiments 2. transitions of physical device from state to state must ‘mirror’ structure of abstract Turing machine states