[_yb2s]

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.

[__MatrixMan__]

I think this is related to the https://en.wikipedia.org/wiki/Busy_beaver game. I count 5 bits on the tape, and BB(5) = 47,176,870 which seams like a tractable number of steps for a modern computer to check.

If I've understood it correctly, this means that any program for this machine which does not halt after 47,176,871 states will run indefinitely.

BB(6) is thought to be incredibly huge, so it's nice that they stopped at 5.

[mmarx]

This machine has 8 states, so (for actual Turing Machines with an unbounded tape) you'd be looking at BB(8). However, since the tape can only store 24 symbols, the machine only has 8 (states) * 4 (tape symbols) * 24 (tape length) = 768 different configurations. Thus, any program will either terminate in at most 768 steps, or loop indefinitely.