The coalgebraic approach to weighted automata: an introduction

In this talk, I will give an overview of how weighted automata can be seen as coalgebras and bialgebras. The coalgebraic approach to weighted automata was developed by Rutten, Bonsangue, Bartels, Silva, Bonchi, and others, and allows us to represent weighted automata as so-called systems of behavioural differential equations, the solution of which is given by the unique mapping into the final coalgebra (or bialgebra). Furthermore, I will discuss the relationship (and differences) with the traditional approach to weighted automata, and mention a number of applications, such as bisimulation techniques as a tool to prove equivalence, and the coinductive stream calculus.