179 research outputs found
When equivalence and bisimulation join forces in probabilistic automata
Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic automata were re-proposed by Segala in 1995 which are more general than Rabin's automata. Bisimulations have been proposed for Segala's automata to characterize the equivalence between them. So far the two notions of equivalences and their characteristics have been studied most independently. In this paper, we consider Segala's automata, and propose a novel notion of distribution-based bisimulation by joining the existing equivalence and bisimilarities. Our bisimulation bridges the two closely related concepts in the community, and provides a uniform way of studying their characteristics. We demonstrate the utility of our definition by studying distribution-based bisimulation metrics, which gives rise to a robust notion of equivalence for Rabin's automata. © 2014 Springer International Publishing Switzerland
Lattice structures for bisimilar Probabilistic Automata
The paper shows that there is a deep structure on certain sets of bisimilar
Probabilistic Automata (PA). The key prerequisite for these structures is a
notion of compactness of PA. It is shown that compact bisimilar PA form
lattices. These results are then used in order to establish normal forms not
only for finite automata, but also for infinite automata, as long as they are
compact.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
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
Probabilistic Bisimulation: Naturally on Distributions
In contrast to the usual understanding of probabilistic systems as stochastic
processes, recently these systems have also been regarded as transformers of
probabilities. In this paper, we give a natural definition of strong
bisimulation for probabilistic systems corresponding to this view that treats
probability distributions as first-class citizens. Our definition applies in
the same way to discrete systems as well as to systems with uncountable state
and action spaces. Several examples demonstrate that our definition refines the
understanding of behavioural equivalences of probabilistic systems. In
particular, it solves a long-standing open problem concerning the
representation of memoryless continuous time by memory-full continuous time.
Finally, we give algorithms for computing this bisimulation not only for finite
but also for classes of uncountably infinite systems
Languages and models for hybrid automata: A coalgebraic perspective
article in pressWe study hybrid automata from a coalgebraic point of view. We show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results. This includes, among other things, notions of bisimulation and behaviour, state minimisation techniques, and regular expression languages.POCI-01-0145-FEDER-016692. RDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016692 and by the PT-FLAD Chair on Smart Cities & Smart Governance at Universidade do Minh
Distribution-based bisimulation for labelled Markov processes
In this paper we propose a (sub)distribution-based bisimulation for labelled
Markov processes and compare it with earlier definitions of state and event
bisimulation, which both only compare states. In contrast to those state-based
bisimulations, our distribution bisimulation is weaker, but corresponds more
closely to linear properties. We construct a logic and a metric to describe our
distribution bisimulation and discuss linearity, continuity and compositional
properties.Comment: Accepted by FORMATS 201
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
Decentralized bisimulation for multiagent systems
Copyright © 2015, International Foundation for Autonomous Agents and Multiagent Systems. The notion of bisimulation has been introduced as a powerful way to abstract from details of systems in the formal verification community. When applying to multiagent systems, classical bisimulations will allow one agent to make decisions based on full histories of others. Thus, as a general concept, classical bisimulations are unrealistically powerful for such systems. In this paper, we define a coarser notion of bisimulation under which an agent can only make realistic decisions based on information available to it. Our bisimulation still implies trace distribution equivalence of the systems, and moreover, it allows a compositional abstraction framework of reasoning about the systems
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