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Diagrammatic Polyhedral Algebra

Authors Filippo Bonchi , Alessandro Di Giorgio , Paweł Sobociński



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Author Details

Filippo Bonchi
  • University of Pisa, Italy
Alessandro Di Giorgio
  • University of Pisa, Italy
Paweł Sobociński
  • Tallinn University of Technology, Estonia

Acknowledgements

The authors have benefited, at the early stage of this work, of enlightening comments and exciting discussions with Guillaume Boisseau. In particular, Guillaume proposed several simplifications to the axiomatisations, showed us the first proof of the generalised spider and the one for its polar.

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Filippo Bonchi, Alessandro Di Giorgio, and Paweł Sobociński. Diagrammatic Polyhedral Algebra. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 40:1-40:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.FSTTCS.2021.40

Abstract

We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of polyhedra.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
  • Theory of computation → Concurrency
Keywords
  • String diagrams
  • Polyhedral cones
  • Polyhedra

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