  Given a complex system with a given interface to the rest of the world, what
does it mean for a the system to behave close to a simpler specification
describing the behavior at the interface? We give several definitions for
useful notions of distances between a complex system and a specification by
combining a behavioral and probabilistic perspective. These distances can be
used to tune a complex system to a specification. We show that our approach can
successfully tune non-linear networked systems to behave like much smaller
networks, allowing us to aggregate large sub-networks into one or two effective
nodes. Finally, we discuss similarities and differences between our approach
and $H_\infty$ model reduction.
