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

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

Bonchi, F; Sobociński, P; Zanasi, F; (2017) The Calculus of Signal Flow Diagrams I: Linear relations on streams. Information and Computation , 252 pp. 2-29. 10.1016/j.ic.2016.03.002. Green open access

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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.

Type:	Article
Title:	The Calculus of Signal Flow Diagrams I: Linear relations on streams
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1016/j.ic.2016.03.002
Publisher version:	https://doi.org/10.1016/j.ic.2016.03.002
Language:	English
Additional information:	This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords:	Signal flow graphString diagramLinear algebraPROPDistributive lawHopf algebraFrobenius algebra
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI:	https://discovery.ucl.ac.uk/id/eprint/1561409