In applications where the notion of observable
behaviour is clear, the most suitable equivalence is usually the one
which is *fully abstract* with respect to this notion of observable
behaviour, i.e. identifies two processes if and only if their
observable behaviour is the same. However, if there is no clarity on
what is observable, a verification in a fully abstract semantics
w.r.t. any notion of observability needs to be redone every time one
discovers that a little bit more can be observed than what was
originally accounted for. Moreover, the soundness of the verification
depends crucially on the right estimation of what can be observed. A
verification (of the equivalence of two processes) in a semantics that
preserves the internal structure of processes, on the other hand, does
not depend on considerations of observability (as long as it is clear
that no more can be observable than this internal structure), and is
automatically valid in any semantics that is fully abstract w.r.t.
some notion of observable behaviour. Now for the simple kind of
processes that are the subject of this paper, the best formalization
of the internal structure of a process appears to be its branching
structure. (However, for more complex systems the internal structure
may involve more, e.g. the *causal structure* of processes.)