189 research outputs found
Approximate reasoning for real-time probabilistic processes
We develop a pseudo-metric analogue of bisimulation for generalized
semi-Markov processes. The kernel of this pseudo-metric corresponds to
bisimulation; thus we have extended bisimulation for continuous-time
probabilistic processes to a much broader class of distributions than
exponential distributions. This pseudo-metric gives a useful handle on
approximate reasoning in the presence of numerical information -- such as
probabilities and time -- in the model. We give a fixed point characterization
of the pseudo-metric. This makes available coinductive reasoning principles for
reasoning about distances. We demonstrate that our approach is insensitive to
potentially ad hoc articulations of distance by showing that it is intrinsic to
an underlying uniformity. We provide a logical characterization of this
uniformity using a real-valued modal logic. We show that several quantitative
properties of interest are continuous with respect to the pseudo-metric. Thus,
if two processes are metrically close, then observable quantitative properties
of interest are indeed close.Comment: Preliminary version appeared in QEST 0
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
Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems
Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of
behavioural pseudometrics for probabilistic transition systems. These
pseudometrics are a quantitative analogue of probabilistic bisimilarity.
Distance zero captures probabilistic bisimilarity. Each pseudometric has a
discount factor, a real number in the interval (0, 1]. The smaller the discount
factor, the more the future is discounted. If the discount factor is one, then
the future is not discounted at all. Desharnais et al. showed that the
behavioural distances can be calculated up to any desired degree of accuracy if
the discount factor is smaller than one. In this paper, we show that the
distances can also be approximated if the future is not discounted. A key
ingredient of our algorithm is Tarski's decision procedure for the first order
theory over real closed fields. By exploiting the Kantorovich-Rubinstein
duality theorem we can restrict to the existential fragment for which more
efficient decision procedures exist
Labelled transition systems as a Stone space
A fully abstract and universal domain model for modal transition systems and
refinement is shown to be a maximal-points space model for the bisimulation
quotient of labelled transition systems over a finite set of events. In this
domain model we prove that this quotient is a Stone space whose compact,
zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree
of bisimilarity such that image-finite labelled transition systems are dense.
Using this compactness we show that the set of labelled transition systems that
refine a modal transition system, its ''set of implementations'', is compact
and derive a compactness theorem for Hennessy-Milner logic on such
implementation sets. These results extend to systems that also have partially
specified state propositions, unify existing denotational, operational, and
metric semantics on partial processes, render robust consistency measures for
modal transition systems, and yield an abstract interpretation of compact sets
of labelled transition systems as Scott-closed sets of modal transition
systems.Comment: Changes since v2: Metadata updat
Equational Reasonings in Wireless Network Gossip Protocols
Gossip protocols have been proposed as a robust and efficient method for
disseminating information throughout large-scale networks. In this paper, we
propose a compositional analysis technique to study formal probabilistic models
of gossip protocols expressed in a simple probabilistic timed process calculus
for wireless sensor networks. We equip the calculus with a simulation theory to
compare probabilistic protocols that have similar behaviour up to a certain
tolerance. The theory is used to prove a number of algebraic laws which
revealed to be very effective to estimate the performances of gossip networks,
with and without communication collisions, and randomised gossip networks. Our
simulation theory is an asymmetric variant of the weak bisimulation metric that
maintains most of the properties of the original definition. However, our
asymmetric version is particularly suitable to reason on protocols in which the
systems under consideration are not approximately equivalent, as in the case of
gossip protocols
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