Tapes as Stochastic Matrices of String Diagrams
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917183347490816 |
|---|---|
| author | Bonchi, Filippo Cioffo, Cipriano Junior |
| author_facet | Bonchi, Filippo Cioffo, Cipriano Junior |
| contents | Tape diagrams provide a graphical notation for categories equipped with two monoidal products, $\otimes$ and $\oplus$, where $\oplus$ is a biproduct. Recently, they have been generalised to handle Kleisli categories of arbitrary monoidal monads. In this work, we show that for the subdistribution monad, tapes are isomorphic to stochastic matrices of subdistributions of string diagrams. We then exploit this result to provide a complete axiomatisation of probabilistic Boolean circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01472 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tapes as Stochastic Matrices of String Diagrams Bonchi, Filippo Cioffo, Cipriano Junior Logic in Computer Science Category Theory Tape diagrams provide a graphical notation for categories equipped with two monoidal products, $\otimes$ and $\oplus$, where $\oplus$ is a biproduct. Recently, they have been generalised to handle Kleisli categories of arbitrary monoidal monads. In this work, we show that for the subdistribution monad, tapes are isomorphic to stochastic matrices of subdistributions of string diagrams. We then exploit this result to provide a complete axiomatisation of probabilistic Boolean circuits. |
| title | Tapes as Stochastic Matrices of String Diagrams |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2601.01472 |