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Rewriting with Frobenius

Rewriting with Frobenius
Rewriting with Frobenius
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.
165-174
ACM
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Gadducci, Fabio
58494b0f-53f3-4751-8a6c-1738b1c14c79
Kissinger, Aleks
b41eacd9-1a0e-44f1-ab52-7ad1741ae6b3
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Gadducci, Fabio
58494b0f-53f3-4751-8a6c-1738b1c14c79
Kissinger, Aleks
b41eacd9-1a0e-44f1-ab52-7ad1741ae6b3
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38

Bonchi, Filippo, Gadducci, Fabio, Kissinger, Aleks, Sobocinski, Pawel and Zanasi, Fabio (2018) Rewriting with Frobenius. In LICS '18 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM. pp. 165-174 . (doi:10.1145/3209108.3209137).

Record type: Conference or Workshop Item (Paper)

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.

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Published date: 9 July 2018
Venue - Dates: Thirty-Third Annual ACM/IEEE Symposium on<br/>Logic in Computer Science (LICS 2018), Oxford, United Kingdom, 2018-07-09 - 2018-07-12

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Local EPrints ID: 422531
URI: http://eprints.soton.ac.uk/id/eprint/422531
PURE UUID: 1b5848c3-d8b2-4816-bb8a-d5b87188ee4b

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Date deposited: 25 Jul 2018 16:30
Last modified: 16 Dec 2019 18:05

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