Stochastic Relations: Foundations for Markov Transition Systems Ernst-Erich Doberkat Conceptual Structures in Practice Pascal Hitzler and Henrik Schärfe Context-Aware Computing and Self-Managing Systems

Stochastic Nondeterminism and Effectivity Functions

This paper investigates stochastic nondeterminism by relating nondeterministic labelled Markov processes and stochastic effectivity functions to each other; the underlying state spaces are continuous. Both generalizations to labelled Markov transition systems have been proposed recently with differing intentions. It turns out that they display surprising similarities and interesting differences...

Semi-pullbacks and Bisimulations in Categories of Stochastic Relations

Factoring stochastic relations

When a system represented through a stochastic model is observed, the equivalence of behavior is described through the observation that equivalent inputs lead to equivalent outputs. This paper has a look at the systems that arise when the stochastic model is factored through the congruence. Congruences may refine each other, and we show that this refinement is reflected through factoring. We al...

Derandomizing probabilistic semantics through Eilenberg-Moore algebras for the Giry monad

A simple language is defined, a probabilistic semantics and a partial correctness logic is proposed in terms of probabilistic relations. It is shown how a derandomized semantics can be constructed through the Eilenberg-Moore algebras. We investigate the category of EilenbergMoore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphism...

Characterizing the Eilenberg-Moore Algebras for a Monad of Stochastic Relations

We investigate the category of Eilenberg-Moore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphisms. The algebras are characterized through convex partitions of the space of all probability measures. Examples are investigated, and it is shown that finite spaces usually do not have algebras at all.