15,537 research outputs found
Compositional Verification and Optimization of Interactive Markov Chains
Interactive Markov chains (IMC) are compositional behavioural models
extending labelled transition systems and continuous-time Markov chains. We
provide a framework and algorithms for compositional verification and
optimization of IMC with respect to time-bounded properties. Firstly, we give a
specification formalism for IMC. Secondly, given a time-bounded property, an
IMC component and the assumption that its unknown environment satisfies a given
specification, we synthesize a scheduler for the component optimizing the
probability that the property is satisfied in any such environment
Verification of Open Interactive Markov Chains
Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation. For this we embed the IMC into a game that is played with the environment. We devise algorithms that enable us to derive bounds on reachability probabilities that are assured to hold in any composition context
Zero-sum stopping games with asymmetric information
We study a model of two-player, zero-sum, stopping games with asymmetric
information. We assume that the payoff depends on two continuous-time Markov
chains (X, Y), where X is only observed by player 1 and Y only by player 2,
implying that the players have access to stopping times with respect to
different filtrations. We show the existence of a value in mixed stopping times
and provide a variational characterization for the value as a function of the
initial distribution of the Markov chains. We also prove a verification theorem
for optimal stopping rules which allows to construct optimal stopping times.
Finally we use our results to solve explicitly two generic examples
Analysing Decisive Stochastic Processes
In 2007, Abdulla et al. introduced the elegant concept of decisive Markov chain. Intuitively, decisiveness allows one to lift the good properties of finite Markov chains to infinite Markov chains. For instance, the approximate quantitative reachability problem can be solved for decisive Markov chains (enjoying reasonable effectiveness assumptions) including probabilistic lossy channel systems and probabilistic vector addition systems with states. In this paper, we extend the concept of decisiveness to more general stochastic processes. This extension is non trivial as we consider stochastic processes with a potentially continuous set of states and uncountable branching (common features of real-time stochastic processes). This allows us to obtain decidability results for both qualitative and quantitative verification problems on some classes of real-time stochastic processes, including generalized semi-Markov processes and stochastic timed
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Statistical verification and differential privacy in cyber-physical systems
This thesis studies the statistical verification and differential privacy in Cyber-Physical Systems. The first part focuses on the statistical verification of stochastic hybrid system, a class of formal models for Cyber-Physical Systems. Model reduction techniques are performed on both Discrete-Time and Continuous-Time Stochastic Hybrid Systems to reduce them to Discrete-Time Markov Chains and Continuous-Time Markov Chains, respectively; and statistical verification algorithms are proposed to verify Linear Inequality LTL and Metric Interval Temporal Logic on these discrete probabilistic models. In addition, the advantage of stratified sampling in verifying Probabilistic Computation Tree Logic on Labeled Discrete-Time Markov Chains is studied; this method can potentially be extended to other statistical verification algorithms to reduce computational costs.
The second part focuses on the Differential Privacy in multi-agent systems that involve share information sharing to achieve overall control goals. A general formulation of the systems and a notion of Differential Privacy are proposed, and a trade-off between the Differential Privacy and the tracking performance of the systems is demonstrated. In addition, it is proved that there is a trade-off between Differential Privacy and the entropy of the unbiased estimator of the private data, and an optimal algorithm to achieve the best trade-off is given
Zero-sum stopping games with asymmetric information
We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples
A Compositional Semantics for Stochastic Reo Connectors
In this paper we present a compositional semantics for the channel-based
coordination language Reo which enables the analysis of quality of service
(QoS) properties of service compositions. For this purpose, we annotate Reo
channels with stochastic delay rates and explicitly model data-arrival rates at
the boundary of a connector, to capture its interaction with the services that
comprise its environment. We propose Stochastic Reo automata as an extension of
Reo automata, in order to compositionally derive a QoS-aware semantics for Reo.
We further present a translation of Stochastic Reo automata to Continuous-Time
Markov Chains (CTMCs). This translation enables us to use third-party CTMC
verification tools to do an end-to-end performance analysis of service
compositions.Comment: In Proceedings FOCLASA 2010, arXiv:1007.499
A Markov Chain Model Checker
Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker ), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of )
A model checker for performance and dependability properties
Markov chains are widely used in the context of
performance and reliability evaluation of systems of various
nature. Model checking of such chains with respect to
a given (branching) temporal logic formula has been proposed
for both the discrete [8] and the continuous time setting
[1], [3]. In this short paper, we describe the prototype
model checker for discrete and continuous-time
Markov chains, where properties are expressed in appropriate
extensions of CTL.We illustrate the general benefits
of this approach and discuss the structure of the tool
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