[Family] Exponential counters have the property that they grow very slowly.
In practice, I have found that having less than 50 tape-extension events in 10,000,000 steps is a good hint that a machine is an exponential counter. A tape-extension event is a time step where the machine visits a cell it had never seen before.
The experiments that led to this heuristic are avaible at the end of this notebook (paragraph “Counting records heuristic”).