7,188 research outputs found
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
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
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
Data-Driven Abstractions for Control Systems
At the intersection of dynamical systems, control theory, and formal methods
lies the construction of symbolic abstractions: these typically represent
simpler, finite-state models whose behaviour mimics the one of an underlying
concrete system but are easier to analyse. Building an abstraction usually
requires an accurate knowledge of the underlying model: this knowledge may be
costly to gather, especially in real-life applications. We aim to bridge this
gap by building abstractions based on sampling finite length trajectories.
Adding the controller degrees of freedom, we newly define the notion of
probabilistic alternating simulation, and provide probably approximately
correct (PAC) guarantees that the constructed abstraction includes all
behaviours of the concrete system and that it is suitable for control design,
for arbitrarily long time horizons, leveraging the scenario theory. Our method
is then tested on several numerical benchmarks
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