Presentation is loading. Please wait.

Presentation is loading. Please wait.

Turing’s halting problem Danny Brown. Barber paradox.

Similar presentations


Presentation on theme: "Turing’s halting problem Danny Brown. Barber paradox."— Presentation transcript:

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 # … # … # … # … ………………… …

13 Cantor’s diagonal argument # … # … # … # … ………………… …

14 Cantor’s diagonal argument # … # … # … # … ………………… #N …

15 Continuum Hypothesis

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


Download ppt "Turing’s halting problem Danny Brown. Barber paradox."

Similar presentations


Ads by Google