The Demonic Product of Probabilistic Relations

The demonic product of two probabilistic relations is defined and investigated. It is shown that the product is stable under bisimulations when the mediating object is probabilistic, and that under some mild conditions the non-deterministic fringe of the probabilistic relations behaves properly: the fringe of the product equals the demonic product of the fringes

A Note on the Coalgebraic Interpretation of Game Logic

We propose a coalgebraic interpretation of game logic, making the results of coalgebraic logic available for this context. We study some properties of a coalgebraic interpretation, showing among others that Aczel's Theorem on the characterization of bisimilar models through spans of morphisms is valid here. We investigate also congruences as those equivalences on the state space which preserve the structure of the model

Stochastic Relations Interpreting Modal Logic

We propose an interpretation of modal logic through stochastic relations, providing a probabilistic complement to the usual nondeterministic interpretations using Kripke models. A simple temporal logic and a logic with a countable number of diamonds illustrate the approach. The main technical result of this paper is a probabilistic analogon to the well-known Hennessy-Milner Theorem characterizing models that have the same theories for their states and bisimilarity as equivalent properties. This requires the study of congruences for stochastic relations that underly the interpretation, for which a general bisimilarity result is also established. The results depend on the existence of semi-pullbacks for stochastic relations over analytic spaces

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 .nite spaces usually do not have algebras at all

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 re.ne each other, and we show that this re.nement is re.ected through factoring. We also show that factoring a factor does not give rise to any new constructions, since we are kept in the realm of factors for the original system. Thus we cannot have in.nite long chains of factors, so that no new behavior can arise from the original system upon factoring (a system and its factors are bisimilar, after all)

Constructing a Heap

The well known algorithms due to Williams and to Floyd for the construction of a heap are considered with respect to their probabilistic properties. For Williams' algorithm the distribution of the heaps generated by this rnethod is investigated by means of a special kind of labeled trees. Floyd's algorithm is considered in greater detail, the expected numbers of interchanges, and comparisons respectively are derived and the leading terms of the asymptotic expansions are given