Bisimulation as congruence in the behavioral setting

@article{Julius2005BisimulationAC,
  title={Bisimulation as congruence in the behavioral setting},
  author={A. A. Julius and A. J. van der Schaft},
  journal={Proceedings of the 44th IEEE Conference on Decision and Control},
  year={2005},
  pages={814-819}
}
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′. 

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