December 23, Wednesday 14:15, Room 570, Education Building
Fixed-point Semantics for Analogue Computation
on Metric Algebras
Lecturer : Jeffry Zucker
Lecturer homepage : http://www.cas.mcmaster.ca/~zucker/
Affiliation :
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 network's inputs and outputs are continuous
streams u: T ® A, and its input-output behaviour is modelled by a functional F on the set C[T,A]
of all continuous streams equipped with the compact-open topology. We give a semantics which involves solving a
fixed point equation over C[T,A] using a contraction
principle. We show that if the module functions
are continuous then so is the network function F. This is significant in terms
of Hadamard's principle. We present a case study
involving mechanical systems.
We
introduce two computation models on C[T,A]: one "concrete", in the
sense of recursive analysis, and the other "abstract", based on a
high level programming language on C[T,A].
We show that these models are equivalent, and that if the module
functions are computable (w.r.t. either of them) then
so is F.
This
is joint work with J.V. Tucker (