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Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
Abstract

Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Mixing Up Nondeterminism and Probability: a preliminary report
, 1999
"... For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of ..."
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Cited by 6 (4 self)
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For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of one component for the system as a whole is treated differently in each interpretation. The same approach is followed for an extension of the language with a parallel operator. The adopted concurrency model is of a distributed nature and assumes that progress is guaranteed if nonfailing components exist. To this end the notion of a takeover of a failing component is incorporated in the transition system. It is shown that the modular way in which the transition system can yield different semantical models applies to this setting as well.
Taking Chances on  and fail: Extending Strong and Probabilistic Bisimulation
, 1999
"... For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition sy ..."
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Cited by 2 (1 self)
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For a process language, featuring nondeterministic and probabilistic choice, a parallel operator and a failure construct, a notion of bisimulation is proposed. As one can interpret recovery from failure with respect to nondeterministic and probabilistic choice in various ways, a single transition system gives rise to several operational models. A uniform way to abstract the `first steps' underlies, for each of these models, the definition of the proposed bisimulation. This bisimulation specializes to ParkMilner bisimulation for the nonprobabilistic fragment of the language on the one hand, and to LarsenSkou bisimulation for the deterministic/probabilistic part of the language, on the other hand. Furthermore, a conditional congruence result is obtained. 1 Introduction Understanding the interplay of nondeterminacy and probability is a key issue in the development of formal techniques for specification and validation of probabilistic programs and protocols. In this paper we study a pr...