Decidability and coincidence of equivalences for concurrency

There are two fundamental problems concerning equivalence relations in con-currency. One is: for which system classes is a given equivalence decidable? The second is: when do two equivalences coincide? Two well-known equivalences are history preserving bisimilarity (hpb) and hereditary history preserving bisimi-larity (hhpb). These are both ‘independence ’ equivalences: they reflect causal dependencies between events. Hhpb is obtained from hpb by adding a ‘back-tracking ’ requirement. This seemingly small change makes hhpb computationally far harder: hpb is well-known to be decidable for finite-state systems, whereas the decidability of hhpb has been a renowned open problem for several years; only recently it has been shown undecidable. The main aim of this thesis is to gain insights into the decidability problem for hhpb, and to analyse when it coincides with hpb; less technically, we might say, to analyse the power of the interplay between concurrency, causality, and conflict. We first examine the backtracking condition, and see that it has two dimen