The area of coalgebra has emerged within theoretical computer science with a unifying
claim: to be the mathematics of computational dynamics. It combines ideas from the theory of …

The Method of Coalgebra: exercises in coinduction Jan Rutten Page 1 The Method of
Coalgebra: exercises in coinduction Jan Rutten February 2019 261 pages ISBN 978-90-6196-568-8 …

Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural
equivalences. We introduce up-to techniques for behavioural metrics between systems …

Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient
proof techniques for checking properties of different kinds of systems. We prove the …

We survey the work on both discrete and continuous-space probabilistic systems as
coalgebras, starting with how probabilistic systems are modeled as coalgebras and followed …

Probabilistic automata (PA) combine probability and nondeterminism. They can be given
different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution …

This paper studies trace-based equivalences for systems combining nondeterministic and
probabilistic choices. We show how trace semantics for such processes can be recovered by …

The monad of convex sets of probability distributions is a well-known tool for modelling the
combination of nondeterministic and probabilistic computational effects. In this work we lift …

We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X->
FX in Set, where the functor F specifies the branching type, we define a framework for …

Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-
coalgebra interaction. They proved to be important for solving systems of corecursive …