  This paper explores the well known approximation approach to decide weak
bisimilarity of Basic Parallel Processes. We look into how different refinement
functions can be used to prove weak bisimilarity decidable for certain
subclasses. We also show their limitations for the general case. In particular,
we show a lower bound of {\omega} \ast {\omega} for the approximants which
allow weak steps and a lower bound of {\omega} + {\omega} for the approximants
that allow sequences of actions. The former lower bound negatively answers the
open question of Jan\v{c}ar and Hirshfeld.
