Bisimulation as congruence in the behavioral setting

We cast the notion of bisimulation in the Willems' behavioral setting. We show that in this setting, bisimulation is also a congruence, as it is known in the field of concurrent processes. Bisimulation is a congruence means if A and A′ are bisimilar systems, then A ∥ B and A′ ∥ B are also bisimilar. Here, the operator ∥ denotes systems composition, and B is any other system that is composed with A or A′.