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 × Ar → 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.