Elegant design pattern for multiple state machines working in concert? [closed]

I'm trying to think of an elegant way to model three state machines that work in concert with one another. For example, say we have these three machines like:

Machine One

A ---> B -.
^          |
|          v
D <------ C

Machine Two,

E <--> F

and Machine Three,

H --> I <--> J

and we we want to write code where Machine One can only transition to state B if Machine Two is in state E and Machine Three is in state I or J. There could be many other rules like that.

Being new to C++, I'm wondering what could be most elegant way to model this kind of behavior of multiple state machines working in concert.