6 papers
Graphical Piecewise-Linear Algebra
Guillaume Boisseau, Robin Piedeleu
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model var…
A String Diagrammatic Axiomatisation of Finite-State Automata
Robin Piedeleu, Fabio Zanasi
We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional…
Contextual Equivalence for Signal Flow Graphs
Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski +1
We extend the signal flow calculus---a compositional account of the classical signal flow graph model of computation---to encompass affine behaviour, and furnish it with a novel op…
Bialgebraic Semantics for String Diagrams
Filippo Bonchi, Robin Piedeleu, Pawel Sobocinski +1
Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational semantics of a system, by means of a distributive law between its syntax (encoded as…
Uniqueness of Composition in Quantum Theory and Linguistics
Bob Coecke, Fabrizio Genovese, Stefano Gogioso +2
We derive a uniqueness result for non-Cartesian composition of systems in a large class of process theories, with important implications for quantum theory and linguistics. Specifi…
Open System Categorical Quantum Semantics in Natural Language Processing
Robin Piedeleu, Dimitri Kartsaklis, Bob Coecke +1
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrz…