Undecidability of the unboundedness problem for specification models a
llowing fifo channels was proved a few years ago by Brand and Zafiropu
lo. The paper investigates a testing approach of that problem. Dealing
with the general framework of systems communicating through fifo chan
nels, we find a sufficient condition for unboundedness based on a rela
tion between the nodes of the reachability tree. The construction of t
he resulting reduced tree can then be applied as well to communicating
finite-state machines as to fifo nets. Moreover, the test extends exi
sting decidability results. As a matter of fact, it becomes a decision
procedure for a class of systems strictly including linear and monoge
neous systems, which are the two essential classes in which decidabili
ty is already known. In order to conclude our study on a practical vie
w, we show that a few modifications of the relation make the test avai
lable for Estelle specifications.