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60
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
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Cited by 128 (26 self)
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Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
PRISM 4.0: Verification of Probabilistic Realtime Systems
"... Abstract. This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and realtime characteristics. In many application do ..."
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Cited by 64 (16 self)
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Abstract. This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and realtime characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is opensource, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicitstate probabilistic model checking library; a discreteevent simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite. 1
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
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Cited by 55 (6 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Numerical vs. statistical probabilistic model checking: An empirical study
 IN 10TH INTERNATIONAL CONFERENCE ON TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS (TACAS’04
, 2004
"... Numerical analysis based on uniformisation and statistical techniques based on sampling and simulation are two distinct approaches for transient analysis of stochastic systems. We compare the two solution techniques when applied to the verification of timebounded until formulae in the temporal st ..."
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Cited by 48 (7 self)
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Numerical analysis based on uniformisation and statistical techniques based on sampling and simulation are two distinct approaches for transient analysis of stochastic systems. We compare the two solution techniques when applied to the verification of timebounded until formulae in the temporal stochastic logic CSL. This study differs from most previous comparisons of numerical and statistical approaches in that CSL model checking is a hypothesis testing problem rather than a parameter estimation problem. We can therefore rely on highly efficient sequential acceptance sampling tests, which enables statistical solution techniques to quickly return a result with some uncertainty. This suggests that statistical techniques can be useful as a first resort during system prototyping, rather than as a last resort as often suggested. We also propose a novel combination of the two solution techniques for verifying CSL queries with nested probabilistic operators.
Model Checking for Probability and Time: From Theory to Practice
 In Proc. Logic in Computer Science
, 2003
"... Probability features increasingly often in software and hardware systems: it is used in distributed coordination and routing problems, to model faulttolerance and performance, and to provide adaptive resource management strategies. Probabilistic model checking is an automatic procedure for establi ..."
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Cited by 47 (1 self)
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Probability features increasingly often in software and hardware systems: it is used in distributed coordination and routing problems, to model faulttolerance and performance, and to provide adaptive resource management strategies. Probabilistic model checking is an automatic procedure for establishing if a desired property holds in a probabilistic model, aimed at verifying probabilistic specifications such as "leader election is eventually resolved with probability 1", "the chance of shutdown occurring is at most 0.01%", and "the probability that a message will be delivered within 30ms is at least 0.75". A probabilistic model checker calculates the probability of a given temporal logic property being satisfied, as opposed to validity. In contrast to conventional model checkers, which rely on reachability analysis of the underlying transition system graph, probabilistic model checking additionally involves numerical solutions of linear equations and linear programming problems. This paper reports our experience with implementing PRISM (www.cs.bham.ac.uk/dxp/ prism/), a Probabilistic Symbolic Model Checker, demonstrates its usefulness in analysing realworld probabilistic protocols, and outlines future challenges for this research direction.
Statistical Model Checking of BlackBox Probabilistic Systems
 In 16th conference on Computer Aided Verification (CAV’04), volume 3114 of LNCS
, 2004
"... We propose a new statistical approach to analyzing stochastic systems against specifications given in a sublogic of continuous stochastic logic (CSL). Unlike past numerical and statistical analysis methods, we assume that the system under investigation is an unknown, deployed blackbox that can be p ..."
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Cited by 41 (7 self)
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We propose a new statistical approach to analyzing stochastic systems against specifications given in a sublogic of continuous stochastic logic (CSL). Unlike past numerical and statistical analysis methods, we assume that the system under investigation is an unknown, deployed blackbox that can be passively observed to obtain sample traces, but cannot be controlled. Given a set of executions (obtained by Monte Carlo simulation) and a property, our algorithm checks, based on statistical hypothesis testing, whether the sample provides evidence to conclude the satisfaction or violation of a property, and computes a quantitative measure (pvalue of the tests) of confidence in its answer; if the sample does not provide statistical evidence to conclude the satisfaction or violation of the property, the algorithm may respond with a "don't know" answer. We implemented our algorithm in a Javabased prototype tool called VeStA, and experimented with the tool using case studies analyzed in [15]. Our empirical results show that our approach may, at least in some cases, be faster than previous analysis methods.
The ins and outs of the probabilistic model checker MRMC
 in Proc. QEST’09
, 2009
"... The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions. Distinguishing features of MRMC are its support for computing time and rewardbounded reachability probabilities, (prop ..."
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Cited by 29 (4 self)
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The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions. Distinguishing features of MRMC are its support for computing time and rewardbounded reachability probabilities, (propertydriven) bisimulation minimization, and precise onthefly steadystate detection. Recent tool features include timebounded reachability analysis for uniform CTMDPs and CSL model checking by discreteevent simulation. This paper presents the tool’s current status and its implementation details. 1.
On statistical model checking of stochastic systems
 In Etessami, K., Rajamani, S.K., eds.: CAV. Volume 3576 of Lecture Notes in Computer Science
, 2005
"... Abstract. Statistical methods to model check stochastic systems have been, thus far, developed only for a sublogic of continuous stochastic logic (CSL) that does not have steady state operator and unbounded until formulas. In this paper, we present a statistical model checking algorithm that also ve ..."
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Cited by 28 (2 self)
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Abstract. Statistical methods to model check stochastic systems have been, thus far, developed only for a sublogic of continuous stochastic logic (CSL) that does not have steady state operator and unbounded until formulas. In this paper, we present a statistical model checking algorithm that also verifies CSL formulas with unbounded untils. The algorithm is based on Monte Carlo simulation of the model and hypothesis testing of the samples, as opposed to sequential hypothesis testing. We have implemented the algorithm in a tool called VESTA, and found it to be effective in verifying several examples. 1
A Bayesian Approach to Model Checking Biological Systems ⋆
"... Abstract. Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been sh ..."
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Cited by 18 (8 self)
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Abstract. Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequential Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Model Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requiring fewer system simulations. Another advantage of our approach is the ability to incorporate prior Biological knowledge about the model being verified. We demonstrate our algorithm on a variety of models from the Systems Biology literature and show that it enables faster verification than stateoftheart techniques, even when no prior knowledge is available. 1
VESTA: A Statistical Modelchecker and Analyzer for Probabilistic Systems
"... Abstract We give a brief overview of the functionality and implementation of a statistical modelchecking and analysis tool VESTA. 1. Overview of VESTA VESTA is a tool for statistical analysis of probabilistic systems. It supports statistical modelchecking [6, 7] and statistical evaluation of expec ..."
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Cited by 17 (0 self)
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Abstract We give a brief overview of the functionality and implementation of a statistical modelchecking and analysis tool VESTA. 1. Overview of VESTA VESTA is a tool for statistical analysis of probabilistic systems. It supports statistical modelchecking [6, 7] and statistical evaluation of expected values of temporal expressions. For modelchecking VESTA uses a sequence of interrelated statistical hypothesis testing to check if a property specified in probabilistic computation tree logic (PCTL) [3] or continuous stochastic logic (CSL) is satisfied by a stochastic model. Furthermore, VESTA supports the statistical computation of expected values of expressions written in a query language called Quantitative Temporal Expressions (or QUATEX in short). We next describe the various components of the tool. Models The analysis algorithms of VESTA are independent of the modelling language for probabilistic systems. VESTA only assumes that it can perform discreteevent simulation of the input probabilistic model. It also assumes that the probability measure associated with the paths of the model is fixed. VESTA allows to plugin any probabilistic modelling language provided that we provide a discreteevent simulator for the modelling language by implementing the following three interface methods: 1. State initialState() : returns the initial state of the model, 2. State nextState(State current) : computes a next state of the model from the current state using discreteevent simulation and returns the computed state, 3. State duplicate(State current) : duplicates the current state and returns it. VESTA currently provides interfaces for two modelling languages: 1. a language to specify discretetime and continuoustime Markov chains. The syntax of this language is closely related to that in PRISM [5], and