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Graphical affine algebra

Graphical affine algebra
Graphical affine algebra

Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably powerful: it can model systems with richer patterns of behaviour such as mutual exclusion-with modules over the natural numbers as semantic domain-or non-passive electrical components-when considering modules over a certain field. Our main technical contribution is a complete axiomatisation for graphical affine algebra over these two interpretations. We also show, as case studies, how graphical affine algebra captures electrical circuits and the calculus of stateless connectors-a coordination language for distributed systems.

1-12
Institute of Electrical and Electronics Engineers Inc.
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Piedeleu, Robin
84e8d041-a00a-44d5-9d7f-101cffd71ee2
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Piedeleu, Robin
84e8d041-a00a-44d5-9d7f-101cffd71ee2
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38

Bonchi, Filippo, Piedeleu, Robin, Sobocinski, Pawel and Zanasi, Fabio (2019) Graphical affine algebra. In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2019. vol. 2019-June, Institute of Electrical and Electronics Engineers Inc. pp. 1-12 . (doi:10.1109/LICS.2019.8785877).

Record type: Conference or Workshop Item (Paper)

Abstract

Graphical linear algebra is a diagrammatic language allowing to reason compositionally about different types of linear computing devices. In this paper, we extend this formalism with a connector for affine behaviour. The extension, which we call graphical affine algebra, is simple but remarkably powerful: it can model systems with richer patterns of behaviour such as mutual exclusion-with modules over the natural numbers as semantic domain-or non-passive electrical components-when considering modules over a certain field. Our main technical contribution is a complete axiomatisation for graphical affine algebra over these two interpretations. We also show, as case studies, how graphical affine algebra captures electrical circuits and the calculus of stateless connectors-a coordination language for distributed systems.

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More information

Accepted/In Press date: 24 June 2019
e-pub ahead of print date: 5 August 2019
Venue - Dates: 34th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2019, Canada, 2019-06-23 - 2019-06-26

Identifiers

Local EPrints ID: 433743
URI: http://eprints.soton.ac.uk/id/eprint/433743
PURE UUID: 1baa04e2-fb9d-4ca8-8be9-1ff52621e601

Catalogue record

Date deposited: 03 Sep 2019 16:30
Last modified: 06 Oct 2020 19:24

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