The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition

Paul Wilson
(University of Southampton)
Fabio Zanasi
(University College London)

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 less 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 a 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.

In Kohei Kishida: Proceedings of the Fourth International Conference on Applied Category Theory (ACT 2021), Cambridge, United Kingdom, 12-16th July 2021, Electronic Proceedings in Theoretical Computer Science 372, pp. 262–275.
Published: 3rd November 2022.

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