Refinement for Signal Flow Graphs

Bonchi, Filippo; Holland, Joshua; Pavlović, Duško; Sobociński, Paweł

doi:10.4230/lipics.concur.2017.24

Cited by 4 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the syntactic side, we extend the signature (1), (2) with a single generator (3) String Diagrammatic Electrical Circuit Theory obtaining a richer string diagrammatic syntax as the arrows of the free prop GAA. Abusing notation, the semantics [−] k : GAA → AffRel k is defined the same way as for GLA on the shared generators, and [ ] k = { (•, 1)}.…”

Section: Graphical Affine Algebra and Electrical Circuitsmentioning

confidence: 99%

See 1 more Smart Citation

String Diagrammatic Electrical Circuit Theory

Boisseau

Sobociński

2022

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for diagrammatic reasoning on circuit diagrams. We demonstrate the power of our approach by giving idiomatic proofs of several textbook results, including the superposition theorem and Thévenin's theorem.

show abstract

Section: Graphical Affine Algebra and Electrical Circuitsmentioning

confidence: 99%

“…Indeed, LinRel k and AffRel k can be considered as ordered props by using set-theoretical inclusion of relations as the homset order. On the syntactic side, it suffices [2] to add a single inequation:…”

Section: Graphical Affine Algebra and Electrical Circuitsmentioning

confidence: 99%

String Diagrammatic Electrical Circuit Theory

Boisseau

Sobociński

2022

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

show abstract

Monoidal Multiplexing

Chantawibul¹,

Sobociński²

2018

Theoretical Aspects of Computing – ICTAC 2018

View full text Add to dashboard Cite

Given a classical algebraic structure-e.g. a monoid or groupwith carrier set X, and given a positive integer n, there is a canonical way of obtaining the same structure on carrier set X n by defining the required operations "pointwise". For resource-sensitive algebra (i.e. based on mere symmetric monoidal, not cartesian structure), similar "pointwise" operations are usually defined as a kind of syntactic sugar: for example, given a comonoid structure on X, one obtains a comultiplication on X ⊗ X by tensoring two comultiplications and composing with an appropriate permutation. This is a specific example of a general construction that we identify and refer to as multiplexing. We obtain a general theorem that guarantees that any equation that holds in the base case will hold also for the multiplexed operations, thus generalising the "pointwise" definitions of classical universal algebra.

show abstract