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

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• 作者：Filippo Bonchi^a ; ^{filippo.bonchi@ens-lyon.fr} ; Paweł Sobociński^b ; ^{ps@ecs.soton.ac.uk} ; Fabio Zanasi^a ; ^{fabio.zanasi@ens-lyon.fr}
• 关键词：Signal flow graph ; String diagram ; Linear algebra ; PROP ; Distributive law ; Hopf algebra ; Frobenius algebra
• 刊名：Information and Computation
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：252
• 期：Complete
• 页码：2-29
• 全文大小：1479 K
• 卷排序：252

文摘

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.