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About this paper
Paul Wilson, Fabio Zanasi
This research transforms string diagrams into efficient, data-parallel computational tools by representing them as structured cospans of ACSets, supporting categories with a Special Frobenius monoid structure to model bidirectional information flow. The approach develops algorithms with linear sequential and logarithmic parallel time complexities for fundamental operations, enabling scalable manipulation of complex diagrams.
Key insights
- A formal categorical isomorphism is established between the proposed ACSet-based diagram representation and free symmetric monoidal categories, both with and without the Special Frobenius structure.
- The concept of 'Frobenius Decomposition' allows any diagram to be factored into elementary Frobenius spider and generator components, facilitating efficient functor application.
- By employing 'wiring maps' and 'ancestor maps,' diagrams can be constructed from Σ-terms in a single, parallel step, bypassing the quadratic complexity of naive inductive methods.
Summary by alphaXiv.
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