So I am reviewing my notes for this problem, and I cant seem to understand how this problem works. Say we have M, and M accepts an input that makes it visit every non-halting state.
I convinced myself that this problem is decidable, but I am having trouble proving so. A rough outline of my answer would be : Assume we have a TM T that has only one halting state, and if it wants to go through all the states it needs to pass through this halt state and we somehow need to show how they cycle through all the states as such.
Any help would be beneficial, thanks!