458 research outputs found
Fluid Model Checking
In this paper we investigate a potential use of fluid approximation
techniques in the context of stochastic model checking of CSL formulae. We
focus on properties describing the behaviour of a single agent in a (large)
population of agents, exploiting a limit result known also as fast simulation.
In particular, we will approximate the behaviour of a single agent with a
time-inhomogeneous CTMC which depends on the environment and on the other
agents only through the solution of the fluid differential equation. We will
prove the asymptotic correctness of our approach in terms of satisfiability of
CSL formulae and of reachability probabilities. We will also present a
procedure to model check time-inhomogeneous CTMC against CSL formulae
Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud
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An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud
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To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud
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To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies
Efficient Parallel Statistical Model Checking of Biochemical Networks
We consider the problem of verifying stochastic models of biochemical
networks against behavioral properties expressed in temporal logic terms. Exact
probabilistic verification approaches such as, for example, CSL/PCTL model
checking, are undermined by a huge computational demand which rule them out for
most real case studies. Less demanding approaches, such as statistical model
checking, estimate the likelihood that a property is satisfied by sampling
executions out of the stochastic model. We propose a methodology for
efficiently estimating the likelihood that a LTL property P holds of a
stochastic model of a biochemical network. As with other statistical
verification techniques, the methodology we propose uses a stochastic
simulation algorithm for generating execution samples, however there are three
key aspects that improve the efficiency: first, the sample generation is driven
by on-the-fly verification of P which results in optimal overall simulation
time. Second, the confidence interval estimation for the probability of P to
hold is based on an efficient variant of the Wilson method which ensures a
faster convergence. Third, the whole methodology is designed according to a
parallel fashion and a prototype software tool has been implemented that
performs the sampling/verification process in parallel over an HPC
architecture
Model Checking CSL for Markov Population Models
Markov population models (MPMs) are a widely used modelling formalism in the
area of computational biology and related areas. The semantics of a MPM is an
infinite-state continuous-time Markov chain. In this paper, we use the
established continuous stochastic logic (CSL) to express properties of Markov
population models. This allows us to express important measures of biological
systems, such as probabilistic reachability, survivability, oscillations,
switching times between attractor regions, and various others. Because of the
infinite state space, available analysis techniques only apply to a very
restricted subset of CSL properties. We present a full algorithm for model
checking CSL for MPMs, and provide experimental evidence showing that our
method is effective.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Stochastic model checking for predicting component failures and service availability
When a component fails in a critical communications service, how urgent is a repair? If we repair within 1 hour, 2 hours, or
n hours, how does this affect the likelihood of service failure? Can a formal model support assessing the impact, prioritisation, and
scheduling of repairs in the event of component failures, and forecasting of maintenance costs? These are some of the questions
posed to us by a large organisation and here we report on our experience of developing a stochastic framework based on a discrete
space model and temporal logic to answer them. We define and explore both standard steady-state and transient temporal logic
properties concerning the likelihood of service failure within certain time bounds, forecasting maintenance costs, and we introduce a
new concept of envelopes of behaviour that quantify the effect of the status of lower level components on service availability. The
resulting model is highly parameterised and user interaction for experimentation is supported by a lightweight, web-based interface
A tutorial on interactive Markov chains
Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud
We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Model Checking Algorithms for Markov Automata
Markov automata constitute a compositional modeling formalism spanning as special cases the models of discrete and continuous time Markov chains, as well as interactive Markov chains and probabilistic automata. This paper discusses the core algorithmic ingredients of a numerical model checking procedure for Markov automata with respect to a PCTL or CSL like temporal logic. The main challenge lies in the computation of time-bounded reachability probabilities, for which we provide a stable approximation scheme
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