We shall discuss the main constituents of the coalgebraic approach to the modelling of dynamical systems and infinite data structures.
(i) A system is modelled by a map s: S -> F(S), where S is the set of the states of the system; F(-) is the system's type (formally a …
read moreWe present a general and constructive method that for a well-behaved function on bitstreams: f: (2^omega)^n --> (2^omega)^m constructs a digital circuit (with n inputs and m outputs) that implements f. More precisely, the method will produce for such f a Mealy automaton that implements f. From …
read moreUsing (stream) differential equations for definitions and coinduction for proofs, we define, analyse, and relate in a uniform way four different algebraic structures on the set of bitstreams (infinite sequences of 0's and 1's), characterising them in terms of the digital circuits they can describe.
read moreIn an earlier report:
F. Arbab, J.J.M.M. Rutten A coinductive calculus of component connectors Technical Report SEN-R0216, CWI, Amsterdam, 2002, pp. 1--17. To appear in the proceedings of WADT 2002. (Available at http://www.cwi.nl/~janr)
a coinductive model for the component connector calculus Reo was …
read moreThis semester at the VUA, I am teaching a minicourse on basic stream calculus with applications to the theory of (signal) flow graphs. In my ACG talk, I shall give a summary of the latter. It will include the following proposition:
a function f: IR^omega -> IR^omega is implementable …
read moreNote that the presentation exceptionally will be given on a Wednesday.
We present an abstract version of (a fragment of) Reo, a framework for building component connectors out of channels, recently introduced by Farhad Arbab A relational model will be constructed in terms of streams, that is, infinite sequences. The …
read moreWe shall elaborate on Sections 13-17 of the recently appeared CWI report
Elements of stream calculus (an extensive exercise in coinduction) SEN-R0120
by treating a number of additional examples of what could be called `coinductive counting'. The main idea is to enumerate the structures to be counted (such as binary …
read moreWe shall elaborate on Sections 13-17 of the recently appeared CWI report
Elements of stream calculus (an extensive exercise in coinduction) SEN-R0120
by treating a number of additional examples of what could be called `coinductive counting'.
The main ideas are to enumerate the structures to be counted (such as binary …
read moreAs an extensive exercise in the use of coinductive techniques, the set of all streams (here: infinite sequences of real numbers) is turned into a calculus in two ways:
the operation of `tail' of a stream is taken as a formal notion of derivative: (s0, s1, s2, ...) ' = (s1, s2, s3 …
read more