A Survey of Compositional Signal Flow Theory

Bonchi, Filippo; Sobociński, Paweł; Zanasi, Fabio

doi:10.1007/978-3-030-81701-5_2

Cited by 5 publications

(3 citation statements)

References 43 publications

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“…While in the previous section we constructed a minimal example from scratch, in this section we take an existing example from the literature where explanations are already used implicitly. Namely, we focus on the research program that has formalised electrical circuits in terms of string diagrams and given them an interpretation in graphical affine algebra [1,4,5,3].…”

Section: Example: Electrical Circuitsmentioning

confidence: 99%

String Diagrams for Layered Explanations

Leo¹,

Zanasi²

2023

Electron. Proc. Theor. Comput. Sci.

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We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood.Our motivating examples come from systems biology, electrical circuit theory, and concurrency. We demonstrate how three explanatory models in these seemingly diverse areas can be all understood uniformly via a graphical calculus of layered props. Layered props allow for a compact visual presentation of the same phenomenon at different levels of precision, as well as the translation between these levels. Notably, our approach allows for partial explanations, that is, for translating just one part of a diagram while keeping the rest of the diagram untouched. Furthermore, our approach paves the way for formal reasoning about counterfactual models in systems biology.

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Section: Example: Electrical Circuitsmentioning

confidence: 99%

String Diagrams for Layered Explanations

Leo¹,

Zanasi²

2023

Electron. Proc. Theor. Comput. Sci.

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“…Many applications of category theory rely on monoidal categories as algebras of processes [26,15,28,18,10,25,11,17,23,27]. Morphisms are compound processes, defined as parallel and sequential compositions of simpler process components.…”

Section: Introductionmentioning

confidence: 99%

Monoidal Width: Capturing Rank Width

Elena

Sobociński

2023

Electron. Proc. Theor. Comput. Sci.

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Monoidal width was recently introduced by the authors as a measure of the complexity of decomposing morphisms in monoidal categories. We have shown that in a monoidal category of cospans of graphs, monoidal width and its variants can be used to capture tree width, path width and branch width. In this paper we study monoidal width in a category of matrices, and in an extension to a different monoidal category of open graphs, where the connectivity information is handled with matrix algebra and graphs are composed along edges instead of vertices. We show that here monoidal width captures rank width: a measure of graph complexity that has received much attention in recent years.

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“…Serving as a process algebra in this sense, it has been used to describe artefacts of a computational nature as arrows of appropriate monoidal categories. Examples include Petri nets [FS18], quantum circuits [CK17,DKPvdW20], signal flow graphs [FS18,BSZ21], electrical circuits [CK22,BS21], digital circuits [GJL17], stochastic processes [Fri20,CJ19] and games [GHWZ18].…”

Section: Introductionmentioning

confidence: 99%

Monoidal Width

Di Lavore,

Sobociński

2023

Logical Methods in Computer Science

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We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition: a monoidal decomposition of a morphism is an expression in the language of monoidal categories, where operations are monoidal products and compositions, that specifies this morphism. Monoidal width penalises the composition operation along ``big'' objects, while it encourages the use of monoidal products. We show that, by choosing the correct categorical algebra for decomposing graphs, we can capture tree width and rank width. For matrices, monoidal width is related to the rank. These examples suggest monoidal width as a good measure for structural complexity of processes modelled as morphisms in monoidal categories.

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A Survey of Compositional Signal Flow Theory

Cited by 5 publications

References 43 publications

String Diagrams for Layered Explanations

String Diagrams for Layered Explanations

Monoidal Width: Capturing Rank Width

Monoidal Width

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