2,259 research outputs found
Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi
Labeled transition systems are typically used to represent the behavior of
nondeterministic processes, with labeled transitions defining a one-step state
to-state reachability relation. This model has been recently made more general
by modifying the transition relation in such a way that it associates with any
source state and transition label a reachability distribution, i.e., a function
mapping each possible target state to a value of some domain that expresses the
degree of one-step reachability of that target state. In this extended
abstract, we show how the resulting model, called ULTraS from Uniform Labeled
Transition System, can be naturally used to give semantics to a fully
nondeterministic, a fully probabilistic, and a fully stochastic variant of a
CSP-like process language.Comment: In Proceedings PACO 2011, arXiv:1108.145
A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences
Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully
probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing
single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing
equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models
Compositional bisimulation metric reasoning with Probabilistic Process Calculi
We study which standard operators of probabilistic process calculi allow for
compositional reasoning with respect to bisimulation metric semantics. We argue
that uniform continuity (generalizing the earlier proposed property of
non-expansiveness) captures the essential nature of compositional reasoning and
allows now also to reason compositionally about recursive processes. We
characterize the distance between probabilistic processes composed by standard
process algebra operators. Combining these results, we demonstrate how
compositional reasoning about systems specified by continuous process algebra
operators allows for metric assume-guarantee like performance validation
Refinement for Probabilistic Systems with Nondeterminism
Before we combine actions and probabilities two very obvious questions should
be asked. Firstly, what does "the probability of an action" mean? Secondly, how
does probability interact with nondeterminism? Neither question has a single
universally agreed upon answer but by considering these questions at the outset
we build a novel and hopefully intuitive probabilistic event-based formalism.
In previous work we have characterised refinement via the notion of testing.
Basically, if one system passes all the tests that another system passes (and
maybe more) we say the first system is a refinement of the second. This is, in
our view, an important way of characterising refinement, via the question "what
sort of refinement should I be using?"
We use testing in this paper as the basis for our refinement. We develop
tests for probabilistic systems by analogy with the tests developed for
non-probabilistic systems. We make sure that our probabilistic tests, when
performed on non-probabilistic automata, give us refinement relations which
agree with for those non-probabilistic automata. We formalise this property as
a vertical refinement.Comment: In Proceedings Refine 2011, arXiv:1106.348
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