@inproceedings{discovery10081075, month = {August}, journal = {Proceedings - Symposium on Logic in Computer Science}, publisher = {IEEE}, year = {2019}, title = {Graphical affine algebra}, address = {Vancouver, BC, Canada}, note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.}, booktitle = {Proceedings of the 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}, url = {https://doi.org/10.1109/LICS.2019.8785877}, author = {Bonchi, F and Piedeleu, R and Sobocinski, P and Zanasi, F}, issn = {1043-6871}, 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} }