eprintid: 10053250
rev_number: 18
eprint_status: archive
userid: 608
dir: disk0/10/05/32/50
datestamp: 2018-08-01 15:59:33
lastmod: 2021-10-18 22:30:12
status_changed: 2018-08-01 15:59:33
type: proceedings_section
metadata_visibility: show
creators_name: Bonchi, F
creators_name: Gadducci, F
creators_name: Kissinger, A
creators_name: Sobocinski, P
creators_name: Zanasi, F
title: Rewriting with Frobenius.
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: Symmetric monoidal categories have become ubiquitous as a formal environment for the analysis of compound systems in a compositional, resource-sensitive manner using the graphical syntax of string diagrams. Recently, reasoning with string diagrams has been implemented concretely via double-pushout (DPO) hypergraph rewriting. The hypergraph representation has the twin advantages of being convenient for mechanisation and of completely absorbing the structural laws of symmetric monoidal categories, leaving just the domain-specific equations explicit in the rewriting system.
In many applications across different disciplines (linguistics, concurrency, quantum computation, control theory,...) the structural component appears to be richer than just the symmetric monoidal structure, as it includes one or more Frobenius algebras. In this work we develop a DPO rewriting formalism which is able to absorb multiple Frobenius structures, thus sensibly simplifying diagrammatic reasoning in the aforementioned applications. As a proof of concept, we use our formalism to describe an algorithm which computes the reduced form of a diagram of the theory of interacting bialgebras using a simple rewrite strategy.
date: 2018-07-12
date_type: published
publisher: ACM
official_url: http://doi.acm.org/10.1145/3209108
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1570782
doi: 10.1145/3209108.3209137
isbn_13: 978-1-4503-5583-4
lyricists_name: Zanasi, Fabio
lyricists_id: FZANA74
actors_name: Zanasi, Fabio
actors_id: FZANA74
actors_role: owner
full_text_status: public
series: https://doi.org/10.1145/3209108.3209137
publication: LICS
place_of_pub: Oxford, United Kingdom
pagerange: 165-174
event_title: LICS '18
book_title: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science
editors_name: Dawar, A
editors_name: Grädel, E
citation:        Bonchi, F;    Gadducci, F;    Kissinger, A;    Sobocinski, P;    Zanasi, F;      (2018)    Rewriting with Frobenius.                     In: Dawar, A and Grädel, E, (eds.) Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science.  (pp. pp. 165-174).  ACM: Oxford, United Kingdom.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10053250/1/paperLICS18.pdf