The extra identifications made in weak bisimulation semantics on top of branching bisimulation semantics can be cumbersome in certain applications of the theory. An example concerns the work of JONSSON & PARROW (1993), mentioned in the introduction. On the other hand we are not aware of a single application where weak bisimulation semantics can be successfully applied, but the extra distinctions made in branching bisimulation semantics pose a problem.

In BOUALI (1992) an example is given were weak
bisimulation semantics works better than branching bisimulation
semantics. The example concerns the minimization of PETERSON's mutual
exclusion algorithm (1981). Here *minimization* means finding an
equivalent process that is as small as possible. In branching
bisimulation semantics this yields a process with 17 states, whereas
in weak bisimulation semantics a process with only 14 states is
obtained. (In fact, using the quasi-branching bisimulation mentioned
in sections 6 and 7 would bring the number of states to 14 already.)
It should be noted however, that weak bisimulation is still far from
optimal for this purpose. *Coupled simulation*, proposed by PARROW &
SJÖDIN (1992), is a generalization of bisimulation semantics to a
setting with silent moves that is coarser than weak bisimulation. It
is completely axiomatized by the laws of weak bisimulation together
with **t(tx+y)=tx+y**. Minimization of Peterson's algorithm in coupled
simulation semantics would yield a process with no more than 9 states,
and using failure semantics (BROOKES, HOARE & ROSCOE (1984), DE NICOLA
& HENNESSY (1984)) would bring it down to 4.

We conjecture that this is illustrative for a general tendency. Coupled simulation has distinct advantages over weak (and branching) bisimulation in applications were the latter notions are too fine. Examples of such applications can be found in PARROW & SJÖDIN (1992) and VAN GLABBEEK & VAANDRAGER (1993). However, whenever weak bisimulation performs better than branching bisimulation, it turns out to be the case that neither of the two notions are really suitable, and coupled simulation, or an even coarser equivalence, is called for.