# On the Algebra of Feedback and Systems with Boundary

## Author

**Piergiulio Katis**, **N. Sabadini** and **R.F.C. Walters**

## Status

Research Report 99-16

Date: 1 July 1999

To appear in Rendiconti del Seminario Matematico di Palermo

## Abstract

The notion of a category-with-feedback is introduced and two main classes of
examples, constructed from input-feedback-output systems and spans of graphs,
are described in detail. After surveying a range of applications to computer
science, we concentrate on two new examples of the algebra: continuous linear
systems, which includes a model of RLC circuits; and a formalization of
double-entry accounting and other systems satisfying the continuity equation.

## Key phrases

monoidal category. bicategory. feedback. concurrency. systems theory.

## AMS Subject Classification (1991)

Primary: 18B20

Secondary: 68Q10, 18D05, 18D10, 93A05

## Content

The paper is available in the following forms:
- PostScript:
- 1999-16.ps.gz (206kB) or
1999-16.ps (539kB)

##### To minimize network load, please choose the smaller gzipped .gz form if
and only if your browser client supports it.

Sydney Mathematics and Statistics