Directions for generalization

• Move to different category of spaces ($\mathsf{Top}$, $\mathsf{Meas}$, etc.)
• Change $\varphi :X\to X$ to $\varphi :X\to M(X)$ for some monad $M$ (such as probability or powerset)
• Consider systems which transition on input $\varphi :A\times X\to X$ and have an output $f:X\to B$ (open Moore machines)

We want clock systems in the most general case: open, nondeterministic systems.