Robert Frank Carslaw Walters > Home > Publications > Pdf Files of Papers > Perugia paper 2000
Piergiulio Katis, N Sabadini, RFC Walters
School of Mathematics and Statistics
University of Sydney
Australia
&
Dipartimento di Scienze dell'Informazione
Universita di Milano, Italy
The authors have introduced elsewhere two complementary algebras
for systems with boundaries the first is the bicategory of circuits or input-feedback-output systems in a monoidal category in which the natural feedback operation has delay, and the second is the compact closed bicategory of spans of graphs in which the natural feedback is instantaneous. The former provides a model of deterministic input driven systems such as asynchronous circuits while the latter provides a model of nondeterministic systems and also specifications of systems. These two bicategories are representatives of two broader classes of algebras and generally there are homomorphisms from the first type of algebra to the second.
Both these classes of algebras may be studied in the context of bicategories with feedback.
It is the purpose of this note to give a brief introduction to and demonstrate the wide range of applicability of these algebras. After surveying the range of examples we concentrate on two new ones. We show that continuous linear systems are an example of the algebra, which includes a model of RLC circuits, and we indicate how the model can be extended to incorporate more general continuous systems. We give a formalization of double entry bookkeeping and other systems satisfying the continuity equation.
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