  We investigate learning collections of languages from texts by an inductive
inference machine with access to the current datum and a bounded memory in form
of states. Such a bounded memory states (BMS) learner is considered successful
in case it eventually settles on a correct hypothesis while exploiting only
finitely many different states.
  We give the complete map of all pairwise relations for an established
collection of criteria of successfull learning. Most prominently, we show that
non-U-shapedness is not restrictive, while conservativeness and (strong)
monotonicity are. Some results carry over from iterative learning by a general
lemma showing that, for a wealth of restrictions (the semantic restrictions),
iterative and bounded memory states learning are equivalent. We also give an
example of a non-semantic restriction (strongly non-U-shapedness) where the two
settings differ.
