The Halting Problem and You!

A simple(st) proof of the halting problem and why it's important to you!

Transcript

1. The Halting Problem and You! Brandon Bradley tweet: @crixdev github: blbradley freenode: bbradley
2. The Problem
3. “... there is no algorithm for deciding whether any given machine, when started from any given initial situation, eventually stops.” - Stephen Kleene
4. decision problem
5. unsolvable with real and abstract computing machines
6. The Proof (by contradiction)
7. suppose we could write a program to solve it
8. let’s call it oracle(p)
9. input - any program code output - halts or does not
10. oracle p yes no halts?
11. some trivial examples
12. p = while(true) oracle p yes no halts?
13. p = pass, nop oracle p yes no halts?
14. sure, but it must work for ANY program
15. let’s make another program!
16. call it deceiver(p)
17. deceiver(p) def deceiver(p): if (oracle(p) == true): while(true): pass else: return true
18. oracle yes no halts? while(true) true p
19. the creative part: refer the deceiver to himself
20. two cases: deceiver loops and deceiver halts
21. oracle yes no halts? while(true) true p p = deceiver loops
22. oracle yes no halts? while(true) true p p = deceiver halts
23. halts => loops loops => halts
24. WAT?
25. deceiver(p) provides a contradiction
26. what’s wrong with this? def deceiver(p): if (oracle(p) == true): while(true): pass else: return true
27. this! def deceiver(p): if (oracle(p) == true): while(true): pass else: return true
28. so, our initial assumption is wrong
29. program oracle(p) can’t be written
30. QED
31. “and You!”
32. there are simple, well- defined problems which exist that can’t be solved
33. many of them ‘reduce’ to the halting problem
34. the ‘canonical’ unsolvable problem
35. intuition is simply not enough
36. algorithms are fun!
37. other undecidable problems • do two compilers/interpreters accept the same languages? • the dead-code problem
38. questions?
39. References & Thanks • Craig Kaplan, Understanding the Halting Problem • Stephen Kleene - Introduction to Metamathematics. 1952. Chapter XIII - Computable Functions. • The Matrix, Warner Bros, © 1999 Thanks to Jason, Emma, all of our speakers, and the rest of our great community!