English

Tapes as Stochastic Matrices of String Diagrams

Logic in Computer Science 2026-01-06 v1 Category Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2601.01472,
  title  = {Tapes as Stochastic Matrices of String Diagrams},
  author = {Filippo Bonchi and Cipriano Junior Cioffo},
  journal= {arXiv preprint arXiv:2601.01472},
  year   = {2026}
}
R2 v1 2026-07-01T08:49:49.907Z