8,864 research outputs found
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
On Zone-Based Analysis of Duration Probabilistic Automata
We propose an extension of the zone-based algorithmics for analyzing timed
automata to handle systems where timing uncertainty is considered as
probabilistic rather than set-theoretic. We study duration probabilistic
automata (DPA), expressing multiple parallel processes admitting memoryfull
continuously-distributed durations. For this model we develop an extension of
the zone-based forward reachability algorithm whose successor operator is a
density transformer, thus providing a solution to verification and performance
evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of
cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing
Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve
in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent
spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of
the formalism, SBRS with sharing, in which the topology is modelled by a directed acyclic graph structure. We
give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model
of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with
possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous
prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model
constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states
modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM.
We illustrate the model on a simple example wireless network with three overlapping signals and we present some
example quantitative properties
Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance
Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft
or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner.
Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''.
The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few.
This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage.
The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling
Stochastic Timed Automata
A stochastic timed automaton is a purely stochastic process defined on a
timed automaton, in which both delays and discrete choices are made randomly.
We study the almost-sure model-checking problem for this model, that is, given
a stochastic timed automaton A and a property , we want to decide whether
A satisfies with probability 1. In this paper, we identify several
classes of automata and of properties for which this can be decided. The proof
relies on the construction of a finite abstraction, called the thick graph,
that we interpret as a finite Markov chain, and for which we can decide the
almost-sure model-checking problem. Correctness of the abstraction holds when
automata are almost-surely fair, which we show, is the case for two large
classes of systems, single- clock automata and so-called weak-reactive
automata. Techniques employed in this article gather tools from real-time
verification and probabilistic verification, as well as topological games
played on timed automata.Comment: 40 pages + appendi
Reaction Networks For Interstellar Chemical Modelling: Improvements and Challenges
We survey the current situation regarding chemical modelling of the synthesis
of molecules in the interstellar medium. The present state of knowledge
concerning the rate coefficients and their uncertainties for the major
gas-phase processes -- ion-neutral reactions, neutral-neutral reactions,
radiative association, and dissociative recombination -- is reviewed. Emphasis
is placed on those reactions that have been identified, by sensitivity
analyses, as 'crucial' in determining the predicted abundances of the species
observed in the interstellar medium. These sensitivity analyses have been
carried out for gas-phase models of three representative, molecule-rich,
astronomical sources: the cold dense molecular clouds TMC-1 and L134N, and the
expanding circumstellar envelope IRC +10216. Our review has led to the proposal
of new values and uncertainties for the rate coefficients of many of the key
reactions. The impact of these new data on the predicted abundances in TMC-1
and L134N is reported. Interstellar dust particles also influence the observed
abundances of molecules in the interstellar medium. Their role is included in
gas-grain, as distinct from gas-phase only, models. We review the methods for
incorporating both accretion onto, and reactions on, the surfaces of grains in
such models, as well as describing some recent experimental efforts to simulate
and examine relevant processes in the laboratory. These efforts include
experiments on the surface-catalysed recombination of hydrogen atoms, on
chemical processing on and in the ices that are known to exist on the surface
of interstellar grains, and on desorption processes, which may enable species
formed on grains to return to the gas-phase.Comment: Accepted for publication in Space Science Review
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