[aroulin]

doesn't the halting problem only hold if you have infinite memory?

[usr1106]

That's probably correct. But any reasonable execution environment has so many states that doing a full enumeration is infeasible.

[rgoulter]

I've seen this argument that 'halting problem is undecideable': http://www.lel.ed.ac.uk/~gpullum/loopsnoop.html

The argument doesn't rely on infinite memory.

[usr1106]

With finite memory and no external inputs an observer can enumerate all possible states.

In real systems external inputs provide an infinite source of "memory" to read from.