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arXiv · 1804.07832

Normalization for planar string diagrams and a quadratic equivalence algorithm

Antonin Delpeuch·Jamie Vicary
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Abstract

In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for connected string diagrams. We use this result to give a linear-time solution to the equivalence problem in the connected case, and a quadratic solution in the general case. We also give a stronger proof of the Joyal-Street coherence theorem, settling Selinger's conjecture on recumbent isotopy.

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Antonin Delpeuch, Jamie Vicary. 2018-04-20. Normalization for planar string diagrams and a quadratic equivalence algorithm. https://doi.org/10.46298/lmcs-18(1%3A10)2022

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