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

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 g...

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Bibliographic Details
Published in:Information and computation 2017-02, Vol.252, p.2-29
Main Authors: Bonchi, Filippo, Sobociński, Paweł, Zanasi, Fabio
Format: Article
Language:English
Subjects:
Distributive law
Frobenius algebra
Hopf algebra
Linear algebra
PROP
Signal flow graph
String diagram
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Summary: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2016.03.002