Computability (Ch 10)

The idea of proving that CanCrash.exe can't exist is pretty mind-bending. This video might be helpful - it walks through the logic on why we can't write a program that detects if a program Halts (stops running at some point):

Also, this Wired article has a nice overview of the problem and argument. It also has a fun Dr. Seuss style poem explaining the Halting Problem:

No general procedure for bug checks will do. Now, I won’t just assert that, I’ll prove it to you. I will prove that although you might work till you drop, you cannot tell if computation will stop.

For imagine we have a procedure called P that for specified input permits you to see whether specified source code, with all of its faults, defines a routine that eventually halts.

...see article for the rest

Optional: Turing Machines

The most amazing feature of Turing's Proof that the Halting Problem and similar decision problems are uncomputable is that he did his work before modern computers existed. He had to invent a theoretical universal computer to make his argument. This machine, known as a Turing Machine is a fundamental model for computation - anything that can be computed with any conceivable computer algorithm can be computed on a Turing machine. This video has a nice introduction to this idea of a Turing Machine: