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28
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 106 (26 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
PRISM 2.0: A tool for probabilistic model checking
 In Proc. 1st International Conference on Quantitative Evaluation of Systems (QEST’04
, 2004
"... This paper gives a brief overview of version 2.0 of PRISM, a tool for the automatic formal verification of probabilistic systems, and some of the case studies to which it has already been applied. 1. ..."
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Cited by 75 (8 self)
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This paper gives a brief overview of version 2.0 of PRISM, a tool for the automatic formal verification of probabilistic systems, and some of the case studies to which it has already been applied. 1.
Implementation of Symbolic Model Checking for Probabilistic Systems
, 2002
"... In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilist ..."
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Cited by 70 (21 self)
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In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilistic model and a speci cation, such as \the message will be delivered with probability 1", \the probability of shutdown occurring is at most 0.02" or \the probability of a leader being elected within 5 rounds is at least 0.98", and can automatically verify if the speci cation is true in the model.
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 61 (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.
A Formal Analysis of Bluetooth Device Discovery
 In Proc. 1st International Symposium on Leveraging Applications of Formal Methods (ISOLA’04
, 2004
"... Abstract. This paper presents a formal analysis of the device discovery phase of the Bluetooth wireless communication protocol. The performance of this process is the result of a complex interaction between several devices, some of which exhibit random behaviour. We use probabilistic model checking ..."
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Cited by 48 (13 self)
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Abstract. This paper presents a formal analysis of the device discovery phase of the Bluetooth wireless communication protocol. The performance of this process is the result of a complex interaction between several devices, some of which exhibit random behaviour. We use probabilistic model checking and, in particular, the tool PRISM to compute the best and worst case expected time for device discovery. We illustrate the utility of performing an exhaustive, lowlevel analysis to produce exact results in contrast to simulation techniques, where additional probabilistic assumptions must be made. We demonstrate an example of how seemingly innocuous assumptions can lead to incorrect performance estimations. We also analyse the effectiveness of improvements made between versions 1.1 and 1.2 of the Bluetooth specification. 1
Model checking probabilistic timed automata with one or two clocks
 In TACAS 2007, volume 4424 of LNCS
, 2007
"... Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems ( ..."
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Cited by 30 (8 self)
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Abstract. Probabilistic timed automata are an extension of timed automata with discrete probability distributions. We consider modelchecking algorithms for the subclasses of probabilistic timed automata which have one or two clocks. Firstly, we show that PCTL probabilistic modelchecking problems (such as determining whether a set of target states can be reached with probability at least 0.99 regardless of how nondeterminism is resolved) are PTIMEcomplete for one clock probabilistic timed automata, and are EXPTIMEcomplete for probabilistic timed automata with two clocks. Secondly, we show that the modelchecking problem for the probabilistic timed temporal logic PTCTL is EXPTIMEcomplete for one clock probabilistic timed automata. However, the corresponding modelchecking problem for the subclass of PTCTL which does not permit both (1) punctual timing bounds, which require the occurrence of an event at an exact time point, and (2) comparisons with probability bounds other than 0 or 1, is PTIMEcomplete. 1
Stochastic games for verification of probabilistic timed automata
 In FORMATS, LNCS 5813
"... Abstract. Probabilistic timed automata (PTAs) are used for formal modelling and verification of systems with probabilistic, nondeterministic and realtime behaviour. For nonprobabilistic timed automata, forwards reachability is the analysis method of choice, since it can be implemented extremely ef ..."
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Cited by 21 (11 self)
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Abstract. Probabilistic timed automata (PTAs) are used for formal modelling and verification of systems with probabilistic, nondeterministic and realtime behaviour. For nonprobabilistic timed automata, forwards reachability is the analysis method of choice, since it can be implemented extremely efficiently. However, for PTAs, such techniques are only able to compute upper bounds on maximum reachability probabilities. In this paper, we propose a new approach to the analysis of PTAs using abstraction and stochastic games. We show how efficient forwards reachability techniques can be extended to yield both lower and upper bounds on maximum (and minimum) reachability probabilities. We also present abstractionrefinement techniques that are guaranteed to improve the precision of these probability bounds, providing a fully automatic method for computing the exact values. We have implemented these techniques and applied them to a set of large case studies. We show that, in comparison to alternative approaches to verifying PTAs, such as backwards reachability and digital clocks, our techniques exhibit superior performance and scalability. 1
Analysing randomized distributed algorithms
 Validation of Stochastic Systems
, 2004
"... Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, thi ..."
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Cited by 14 (2 self)
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Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, this comes at a cost: the analysis of such systems become very complex, particularly in the context of distributed computation. This arises through the interplay between probability and nondeterminism. To prove a randomized distributed algorithm correct one usually involves two levels: classical, assertionbased reasoning, and a probabilistic analysis based on a suitable probability space on computations. In this paper we describe a number of approaches which allows us to verify the correctness of randomized distributed algorithms. 1
Trace Machines for Observing ContinuousTime Markov Chains
 in Proc. of the 3rd Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), ENTCS
, 2005
"... In this paper, we study several lineartime equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuoustime Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of pushbutton experiments with appropri ..."
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Cited by 12 (1 self)
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In this paper, we study several lineartime equivalences (Markovian trace equivalence, failure and ready trace equivalence) for continuoustime Markov chains that refer to the probabilities for timed execution paths. Our focus is on testing scenarios by means of pushbutton experiments with appropriate trace machines and a discussion of the connections between the equivalences. For Markovian trace equivalence, we provide alternative characterizations, including one that abstracts away from the time instances where actions are observed, but just reports on the average sojourn times in the states. This result is used for a reduction of the question whether two finitestate continuoustime Markov chains are Markovian trace equivalent to the probabilistic trace equivalence problem for discretetime Markov chains (and the latter is known to be solvable in polynomial time).
Model Checking for Probabilistic Timed Systems
 In Validation of Stochastic Systems – A Guide to Current Research, volume 2925 of LNCS
, 2004
"... Application areas such as multimedia equipment, communication protocols and networks often feature systems which exhibit both probabilistic and timed behaviour. In this paper, we consider analysis of such probabilistic timed systems using the technique of model checking, in which it is verified ..."
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Cited by 5 (0 self)
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Application areas such as multimedia equipment, communication protocols and networks often feature systems which exhibit both probabilistic and timed behaviour. In this paper, we consider analysis of such probabilistic timed systems using the technique of model checking, in which it is verified automatically whether a system satisfies a certain desired property. In order to describe formally probabilistic timed systems, we consider probabilistic extensions of timed automata, such as realtime probabilistic processes, probabilistic timed automata and continuous probabilistic timed automata, the underlying semantics of each of which is an infinitestate structure. For each formalism, we consider how the wellknown region equivalence relation can be used to reduce the infinite statespace model into a finitestate system, which can then be used for model checking.