Bisimulation trees and the decidability of weak bisimulations

The development of 'bisimulation trees' as a means to prove decidability of weak bisimulation for restricted classes of BPP and BPA was presented. The notion of a bisimulation tree is a very useful way of presenting the information that concerns a particular notion of bisimulation and a pair of processes which needs to be checked. In the commutative case of BPP if the bisimulation is a congruence and if the tree is finitely branching then large pairs of processes in the tree can be replaced by smaller pairs. In the noncommutative case of totally normed BPA the tree is modified by decomposing large pairs in the tree. If the bisimulation supports unique decomposition in the class then the new finite tree encodes the same information as the old one.