  The relationships between various equivalences on configuration structures,
including interleaving bisimulation (IB), step bisimulation (SB) and hereditary
history-preserving (HH) bisimulation, have been investigated by van Glabbeek
and Goltz (and later Fecher). Since HH bisimulation may be characterised by the
use of reverse as well as forward transitions, it is of interest to investigate
forms of IB and SB where both forward and reverse transitions are allowed. We
give various characterisations of reverse SB, showing that forward steps do not
add extra power. We strengthen Bednarczyk's result that, in the absence of
auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that
we need only exclude auto-concurrent events at the same depth in the
configuration.
