This paper investigates conditions that must be satisfied by an FSM for the existence
of input sequences that can be applied in a distributed test architecture
without encountering controllability and observability problems and without
using external coordination messages. Such conditions have two potential values.
First, they can be used to determine whether we require coordination
messages and thus a network that connects the testers. Second, if we wish to
avoid the use of coordination messages in testing then these conditions can be
seen as testability conditions that can inform the design process. Results given
in this paper differ from those in the following ways. First, the conditions
are strictly weaker than those in since we are less restrictive in the
ways we achieve our goals. Second, only considered observability problems;
we consider both controllability and observability problems. In addition,
only considered a particular type of observability problem and we generalize
this. Finally, we investigate the situation in which we need only add input
sequences to complement a given test/checking sequence ρ and prove that the
conditions for this problem are equivalent to those for the original problem