There still is no shortcut -you will still need to actually compute out those states to see how long they run. The fact that for very simple machines this is possible on modern computers does not avoid or solve the halting problem.
I’m not even sure if that is actually possible on this machine even- I suppose it depends on how many bits on the tape, and rapidly becomes impossible to compute after a pretty small number of bits.
But yes- a particular program must eventually either halt or loop back to a state it already was in, which confirms non halting.
I’m not even sure if that is actually possible on this machine even- I suppose it depends on how many bits on the tape, and rapidly becomes impossible to compute after a pretty small number of bits.
But yes- a particular program must eventually either halt or loop back to a state it already was in, which confirms non halting.