We analyze iterative learning in the limit from positive data with the additional information provided by a
. The simplest
of counter provides the current iteration number (counting up from 0 to infinity), which is known to improve learning power over plain iterative learning.
We introduce five other (weaker) counter types, for example only providing some unbounded and non-decreasing sequence of numbers. Analyzing these types allows for understanding what properties of a counter can benefit learning.
For the iterative setting, we completely characterize the relative power of the learning criteria corresponding to the counter types. In particular, for our types, the only properties improving learning power are
Furthermore, we show that each of our types of counter improves learning power over weaker ones in
settings, and that, for iterative learning criteria with one of these types of counter, separations of learning criteria are necessarily witnessed by classes containing only infinite languages.