  A standard contextual equivalence for process algebras is strong barbed
congruence. Configuration structures are a denotational semantics for processes
in which one can define equivalences that are more discriminating, i.e. that
distinguish the denotation of terms equated by barbed congruence. Hereditary
history preserving bisimulation (HHPB) is such a relation. We define a strong
back and forth barbed congruence using a reversible process algebra and show
that the relation induced by the back and forth congruence is equivalent to
HHPB, providing a contextual characterization of HHPB.
