Normalization for planar string diagrams and a quadratic equivalence algorithm

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 linea...

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Bibliographic Details
Published inLogical methods in computer science Vol. 18, Issue 1
Main Authors Delpeuch, Antonin, Vicary, Jamie
Format Journal Article
LanguageEnglish
Published Logical Methods in Computer Science e.V 01.01.2022
Subjects
computer science - logic in computer science
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ISSN1860-5974
1860-5974
DOI10.46298/lmcs-18(1:10)2022

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Summary: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.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-18(1:10)2022