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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| Published in | Logical methods in computer science Vol. 18, Issue 1 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Logical Methods in Computer Science e.V
01.01.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1860-5974 1860-5974 |
| DOI | 10.46298/lmcs-18(1:10)2022 |
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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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Vicary, Jamie Delpeuch, Antonin |
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| Snippet | 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-... 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-... |
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| Title | Normalization for planar string diagrams and a quadratic equivalence algorithm |
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