  Patterns provide a concise, syntactic way of describing a set of strings, but
their expressive power comes at a price: a number of fundamental decision
problems concerning (erasing) pattern languages, such as the membership problem
and inclusion problem, are known to be NP-complete or even undecidable, while
the decidability of the equivalence problem is still open; in learning theory,
the class of pattern languages is unlearnable in models such as the
distribution-free (PAC) framework (if $\mathcal{P}/poly \neq
\mathcal{NP}/poly$). Much work on the algorithmic learning of pattern languages
has thus focussed on interesting subclasses of patterns for which positive
learnability results may be achieved. A natural restriction on a pattern is a
bound on its variable frequency -- the maximum number $m$ such that some
variable occurs exactly $m$ times in the pattern. This paper examines the
effect of limiting the variable frequency of all patterns belonging to a class
$\Pi$ on the worst-case minimum number of labelled examples needed to uniquely
identify any pattern of $\Pi$ in cooperative teaching-learning models. Two such
models, the teaching dimension model as well as the preference-based teaching
model, will be considered.
