Elsevier

Information and Computation

Volume 252, February 2017, Pages 2-29
Information and Computation

The Calculus of Signal Flow Diagrams I: Linear relations on streams

https://doi.org/10.1016/j.ic.2016.03.002Get rights and content
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Abstract

We introduce a graphical syntax for signal flow diagrams based on the language of symmetric monoidal categories. Using universal categorical constructions, we provide a stream semantics and a sound and complete axiomatisation.

A certain class of diagrams captures the orthodox notion of signal flow graph used in control theory; we show that any diagram of our syntax can be realised, via rewriting in the equational theory, as a signal flow graph.

Keywords

Signal flow graph
String diagram
Linear algebra
PROP
Distributive law
Hopf algebra
Frobenius algebra

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