The Calculus of Signal Flow Diagrams I: Linear relations on streams
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- 作者：Filippo Bonchi<sup>asup><sup> ; sup><sup>filippo.bonchi@ens-lyon.frsup> ; Paweł Sobociński<sup>bsup><sup> ; sup><sup>ps@ecs.soton.ac.uksup> ; Fabio Zanasi<sup>asup><sup> ; sup><sup>fabio.zanasi@ens-lyon.frsup>
- 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.