Interacting Hopf Algebras: the theory of linear systems

Tuesday, February 26, 2019

2.30 p.m.

ISI seminar room 1st floor

Prof. Filippo Bonchi University of Pisa

Signal Flow Graphs (SFGs) were introduced in the 1940s by Shannon as a formal circuit model of a class of simple analog computing machines. They are a common abstraction in control theory and signal processing, used for modelling physical systems and their controllers. While Signal Flow Graphs are usually presented as combinatorial structures, in this talk we take a purely algebraic outlook: we provide a string diagrammatic syntax for SFGs and a sound and complete axiomatisation of their Laurent-Series semantics. With tiny variations to the syntax and to the axioms, we are able to characterise other structures that appears to be fundamental in different fields, like Petri nets, passive and non-passive electrical circuits, the ZX calculus (a diagrammatic language for Quantum Mechanics) and Graphical Linear Algebras (

After his Ph.D (Pisa, 2008), Filippo Bonchi has been ERCIM fellow at CWI (Amsterdam) and École polytechnique (Paris). From 2010 to 2017, he worked at École Normale Supérieure (Lyon) as CNRS researcher. In 2018, he moved back to Pisa as Associate Professor. His research interests stand in the meet of Logic, Algebra and Theoretical Computer Science, with particular focus on Coinduction, Coalgebras, String Diagrams and, more generally, Category Theory. He contributed in a large variety of topics, including Automata Theory, Programming Languages, Abstract Interpretation, Algorithms for Model Checking, Data Bases and Relational Algebra and, more recently, the compositional study of Dynamical Systems (such as Signal Flow Graphs, Petri nets, passive and non-passive Electrical circuits). He regularly serves as PC members in top-class conferences of Theoretical Computer Science and has been chairing the Conference on ALgebra and COalgebra in computer science. His paper "Hacking Non-Determinism with Induction and Coinduction" appeared as cover story for Communication of the ACM.