6 research outputs found
Deciding bisimilarities on distributions
Probabilistic automata (PA) are a prominent compositional concurrency model. As a way to justify property-preserving abstractions, in the last years, bisimulation relations over probability distributions have been proposed both in the strong and the weak setting. Different to the usual bisimulation relations, which are defined over states, an algorithmic treatment of these relations is inherently hard, as their carrier set is uncountable, even for finite PAs. The coarsest of these relation, weak distribution bisimulation, stands out from the others in that no equivalent state-based characterisation is known so far. This paper presents an equivalent state-based reformulation for weak distribution bisimulation, rendering it amenable for algorithmic treatment. Then, decision procedures for the probability distribution-based bisimulation relations are presented
Revisiting Weak Simulation for Substochastic Markov Chains
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The Power of Convex Algebras
Probabilistic automata (PA) combine probability and nondeterminism. They can
be given different semantics, like strong bisimilarity, convex bisimilarity, or
(more recently) distribution bisimilarity. The latter is based on the view of
PA as transformers of probability distributions, also called belief states, and
promotes distributions to first-class citizens.
We give a coalgebraic account of the latter semantics, and explain the
genesis of the belief-state transformer from a PA. To do so, we make explicit
the convex algebraic structure present in PA and identify belief-state
transformers as transition systems with state space that carries a convex
algebra. As a consequence of our abstract approach, we can give a sound proof
technique which we call bisimulation up-to convex hull.Comment: Full (extended) version of a CONCUR 2017 paper, to be submitted to
LMC