3 research outputs found
Refinement for Signal Flow Graphs
The symmetric monoidal theory of Interacting Hopf Algebras provides a sound and complete axiomatisation for linear relations over a given field. As is the case for ordinary relations, linear relations have a natural order that coincides with inclusion. In this paper, we give a presentation for this ordering by extending the theory of Interacting Hopf Algebras with a single additional inequation. We show that the extended theory gives rise to an abelian bicategory - a concept due to Carboni and Walters - and highlight similarities with the algebra of relations. Most importantly, the ordering leads to a well-behaved notion of refinement for signal flow graphs
A Finite Axiomatisation of Finite-State Automata Using String Diagrams
We develop a fully diagrammatic approach to finite-state automata, based on
reinterpreting their usual state-transition graphical representation as a
two-dimensional syntax of string diagrams. In this setting, we are able to
provide a complete equational theory for language equivalence, with two notable
features. First, the proposed axiomatisation is finite. Second, the Kleene star
is a derived concept, as it can be decomposed into more primitive algebraic
blocks.Comment: arXiv admin note: text overlap with arXiv:2009.1457