J.V. Tucker and J.I. Zucker (2007):
**Computability of analog networks**.
*Theoretical Computer Science*, **371**, 115-146.
[preprint.pdf,
PDF via ScienceDirect]

**Abstract.**
We define a general concept of a network of analogue processing units
connected by analogue channels, processing data from a metric space A,
and operating with respect to a global continuous clock T, modelled by
the set of non-negative real numbers. The inputs and output of a network
are continuous streams u: T→ A,
and the input-output behaviour of a
network with system parameters from A^{r} is
modelled by a functional of the form

Φ:
A^{r} × C[T,A]^{p} → C[T,A]^{q}
(p,q>0, r≥0)

where C[T,A] is the set of all continuous streams equipped with the
compact-open topology. We give an equational specification
of the network, and a semantics which involves solving
a fixed point equation
over C[T,A], using a contraction principle based on the fact that C[T,A]
can be approximated locally by metric spaces.
We show that if the
module functions are continuous then so is the network function Φ.
We analyse in detail two case
studies involving mechanical systems.
Finally, we introduce a custom-made
concrete computation theory over C[T,A] and show that if the
module functions are concretely computable then so is Φ.