1. # The Coalgebraic Approach

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 …

2. # Automata, Bitstream functions, and Circuits

We 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 …

3. # The Differential Calculus of Bitstreams

Using (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.

4. # Modelling component connectors in Reo by constraint automata

In 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 …

5. # Streams and stream circuits (a coinductive calculus of signal flow graphs)

This 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 …

6. # C-six: constructing a coinductive and compositional calculus of component connectors

Note 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 …

7. # Coinductive counting with weighted automata and continued fractions - part 2

We 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 …

8. # Coinductive counting with weighted automata and continued fractions - part 1

We 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 …