  We investigate the teaching of infinite concept classes through the effect of
the learning bias (which is used by the learner to prefer some concepts over
others and by the teacher to devise the teaching examples) and the sampling
bias (which determines how the concepts are sampled from the class). We analyse
two important classes: Turing machines and finite-state machines. We derive
bounds for the biased teaching dimension when the learning bias is derived from
a complexity measure (Kolmogorov complexity and minimal number of states
respectively) and analyse the sampling distributions that lead to finite
expected biased teaching dimensions. We highlight the existing trade-off
between the bound and the representativeness of the sample, and its
implications for the understanding of what teaching rich concepts to machines
entails.
