Zanasi, F;
(2018)
Rewriting in Free Hypegraph Categories.
In: Kehrer, T and Miller, A, (eds.)
Proceedings of the Workshop on Graphs as Models 2017 (GAM ’17).
(pp. pp. 16-30).
Cornell University Press
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Abstract
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius structures recently appeared in cross-disciplinary applications, including the study of quantum processes, dynamical systems and natural language processing. In this work we give a combinatorial characterisation of arrows of a free hypergraph category as cospans of labelled hypergraphs and establish a precise correspondence between rewriting modulo Frobenius structure on the one hand and double-pushout rewriting of hypergraphs on the other. This interpretation allows to use results on hypergraphs to ensure decidability of confluence for rewriting in a free hypergraph category. Our results generalise previous approaches where only categories generated by a single object (props) were considered.
| Type: | Proceedings paper |
|---|---|
| Title: | Rewriting in Free Hypegraph Categories |
| Event: | Workshop on Graphs as Models 2017 (GAM ’17) |
| Location: | Uppsala, Sweden |
| Dates: | 23rd April 2017 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4204/EPTCS.263.2 |
| Publisher version: | https://arxiv.org/abs/1712.09495v2 |
| Language: | English |
| Additional information: | © F. Zanasi 2017. This work is licensed under the Creative Commons Attribution License (https://creativecommons.org/licenses/by/3.0/). |
| Keywords: | Logic in Computer Science, Distributed, Parallel, and Cluster Computing, Data Structures and Algorithms, Software Engineering |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10047141 |
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