
Bialgebraic Semantics for String Diagrams
Turi and Plotkin's bialgebraic semantics is an abstract approach to spec...
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String Diagram Rewrite Theory II: Rewriting with Symmetric Monoidal Structure
Symmetric monoidal theories (SMTs) generalise algebraic theories in a wa...
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Representing Matrices Using Algebraic ZXcalculus
Elementary matrices play an important role in linear algebra application...
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Functorial String Diagrams for ReverseMode Automatic Differentiation
We enhance the calculus of string diagrams for monoidal categories with ...
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Normal forms for planar connected string diagrams
In the graphical calculus of planar string diagrams, equality is generat...
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Causal Inference by String Diagram Surgery
Extracting causal relationships from observed correlations is a growing ...
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A Foundation for Ledger Structures
This paper introduces an approach to constructing ledger structures for ...
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The Cost of Compositionality: A HighPerformance Implementation of String Diagram Composition
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much fewer attention has been given to their algorithmic properties, and efficient implementations of diagrammatic reasoning are almost an unexplored subject. This work intends to be a contribution in such direction. We introduce a data structure representing string diagrams in terms of adjacency matrices. This encoding has the key advantage of providing simple and efficient algorithms for composition and tensor product of diagrams. We demonstrate its effectiveness by showing that the complexity of the two operations is linear in the size of string diagrams. Also, as our approach is based on basic linear algebraic operations, we can take advantage of heavily optimised implementations, which we use to measure performances of string diagrammatic operations via several benchmarks.
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