Science Forums 2

[Boof-head]

Halting of algorithms is an "algorithmic problem".

Consider the fact that designing and building a modern electronic computer is algorithmic; it's a process that halts when "a viable, working computer" exists; or when it's plugged in and switched on, i.e. tested.

The test is another algorithm, which halts when the test is successful, or when the faulty machine halts - perhaps catastrophically in a big cloud of smoke.

However, Alan Turing proved that there is no way to determine with certainty if a given algorithm will halt - the only way to find out is to test the machine, or build it (so you can test it). The halting problem is well-understood.

Check out Godel's incompleteness theorem (which you'll see is - consistently - an incomplete theory).