J.V. Tucker and J.I. Zucker (2005):

**A Network Model of Analogue Computation over Metric Algebras**.

*New Computational Paradigms: First Conference on Computability
in Europe, CiE 2005, Amsterdam, June 2005: Proceedings*,
ed. S.B. Cooper, B. Löwe, and L. Torenvliet.

Lecture Notes in Computer Science **3526**,
Springer-Verlag, 515-529.

[preprint.pdf,
PDF via SpringerLink]

**Abstract**.
We define a general concept of a network of analog modules
connected by channels, processing data from a metric space A,
and operating with respect to a global continuous clock T.
The inputs and outputs of the network
are continuous streams u:T->A,
and the input-output behaviour of the
network with system parameters from A is modelled by a function

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

where C[T,A] is the set of all continuous streams of A-data 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 by metric spaces.
We analyse a case study involving a mechanical system.
Finally, we introduce a custom-made
concrete computation theory over C[T,A] and show that if the
modules are concretely computable then so is the function Φ.