Yes, the halting problem can be solved for any programs which can only exist in a finite number of states, but most common definitions of a program would includ

Yes, the halting problem can be solved for any programs which can only exist in a finite number of states, but most common definitions of a program would include things such turning machines, which can hold an infinite number of states. Really it comes down to the semantics and bounds of the problem. However I think the most interesting result is mine :P