[Theory] Halting problem

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Just to be clear about this, the halting problem is only unsolvable for Turing
machines.
That is, a machine with a tape that extends or is indefinitely extensible to
the right.[wikipedia:Turing machine]

In the more general limited-memory setup it is actually quite simple to solve
the Halting problem:
1. Save every state of the system.
2. If the program ends, the program Halts -> done.
2. For every state, check to if it has been saved before.
 If so, the program loops -> done.
3. Wait until all states are saved, the program Halts -> done.

Simple in theory that is :)