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1

Bisimulation Cuts For Structuring Markov Transition Systems

Doberkat E.-E.

Fundamenta Informaticae

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2016

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Vol. 149, nr 4

363--383

EN

In Universal Algebra the structure of congruences for algebraic systems is fairly well investigated, and the relationship to the structure of the underlying system proper is well known. We propose a first step into this direction for studying the structure of congruences for stochastic relations. A Galois connection to a certain class of Boolean σ-algebras is exploited, atoms and antiatoms are identified, and it is show that a σ-basis exists. These constructions are applied to the problem of finding bisimulation cuts of a congruence. It cuts the relation through a span of morphisms with a minimum of joint events.

2

Tracing Relations Probabilistically

Doberkat E.-E.

Fundamenta Informaticae

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2005

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Vol. 65, nr 3

193--209

EN

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We show that the construction of traces for both kinds of relations follows the same principles of construction. Representations of measurable trees in terms of probabilistic relations are given. This shows that stochastic relations may serve as refinements of their non-deterministic counterparts. A convexity argument formalizes the observation that non-deterministic system descriptions are underspecified when compared to probabilistic ones. The mathematical tools come essentially from the theory of measurable selections.

3

Tracing Relations Probabilistically

Doberkat E.-E.

Fundamenta Informaticae

|

2005

|

Vol. 66, nr 3

259--275

EN

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We show that the construction of traces for both kinds of relations follows the same principles of construction. Representations of measurable trees in terms of probabilistic relations are given. This shows that stochastic relations may serve as refinements of their non-deterministic counterparts. A convexity argument formalizes the observation that non-deterministic system descriptions are underspecified when compared to probabilistic ones. The mathematical tools come essentially from the theory of measurable selections.