Download presentation

Presentation is loading. Please wait.

Published byHector Shadrick Modified over 2 years ago

1
Turing’s halting problem Danny Brown

2
Barber paradox

3
Barber program BARBER(p) If SHAVE(p,p) = N Then SHAVE(barber,p) = Y Else SHAVE(barber,p) = N END

4
Barber program What happens when we compute BARBER(barber)?

5
Barber program BARBER(barber) If SHAVE(barber,barber) = N Then SHAVE(barber,barber) = Y Else SHAVE(barber,barber) = N END

6
Barber program …so what’s the conclusion?

7
Halting program TEST(p) If HALT(p,p) = N Then HALT(test,p) = Y Else HALT(test,p) = N END

8
Halting program TEST(p) If HALT(p,p) = N Then HALT(test,p) = Y STOP Else LOOP END

9
Halting program TEST(test)…?

10
Halting program TEST(test) If HALT(test,test) = N Then HALT(test,test) = Y STOP Else LOOP END

11
Halting program …so what’s the conclusion?

12
Cantor’s diagonal argument #10.3521… #20.1150… #30.6241… #40.5388… ………………… …

13
Cantor’s diagonal argument #10.3521… #20.1150… #30.6241… #40.5388… ………………… …

14
Cantor’s diagonal argument #10.3521… #20.1150… #30.6241… #40.5388… ………………… #N+10.1211…

15
Continuum Hypothesis

16
Can’t be disproved (Godel 1940) …and can’t be proved (Cohen 1963)

Similar presentations

OK

The Scientific Method. Problem or Scientific Question –Must be testable –Can’t prove something doesn’t exist.

The Scientific Method. Problem or Scientific Question –Must be testable –Can’t prove something doesn’t exist.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sources of water pollution Ppt on power trading in india Ppt on tsunami early warning system Ppt on prepaid energy meter Ppt on bodybuilding Ppt on sources of energy for class 8th Ppt on secret of success Ppt on ecology and environment Free ppt on moving coil galvanometer experiment Ppt on fire extinguisher types video