The definition of open bisimilarity on $\chi$-processes does not give
rise to
a sensible relation on the $\chi$-processes with the mismatch operator.
The paper proposes ground open bisimilarity as a principal open
bisimilarity on the $\chi$-processes with the mismatch operator.
This equivalence is equivalent to the relation derived from a simple
bisimulation
by closing under certain contexts. The algebraic properties of the
ground open
congruence is studied. The paper also takes a close look at barbed
congruence.
This relation is similar to the ground congruence.
The precise relationship between the two is worked out.
It is shown that the sound and complete system for the ground congruence
can be obtained by removing one tau law from the complete system for the
barbed congruence.
