  Senizergues has proved that language equivalence is decidable for disjoint
epsilon-deterministic PDA. Stirling has showed that strong bisimilarity is
decidable for PDA. On the negative side Srba demonstrated that the weak
bisimilarity is undecidable for normed PDA. Later Jancar and Srba established
the undecidability of the weak bisimilarity for disjoint epsilon-pushing PDA
and disjoint epsilon-popping PDA. These decidability and undecidability results
are extended in the present paper. The extension is accomplished by looking at
the equivalence checking issue for the branching bisimilarity of several
variants of PDA.
