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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
Stochastic Hybrid Systems: Application to Communication Networks
 in Hybrid Systems: Computation and Control, ser. Lect. Notes in Comput. Science
, 2004
"... Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continu ..."
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Cited by 51 (14 self)
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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for PiecewiseDeterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for onoff TCP flows that considers both the congestionavoidance and slowstart modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finitedimensional model. This model shows that, for transfersize distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms. 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 50 (18 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 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.
Probabilistic model checking of the IEEE 802.11 wireless local area network protocol
 Proc. 2nd Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification (PAPM/PROBMIV’02), volume 2399 of LNCS
, 2002
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Automatic Verification of the IEEE1394 Root Contention Protocol with KRONOS and PRISM
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
"... We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kro ..."
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Cited by 23 (10 self)
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We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kronos to perform a symbolic forward reachability analysis to generate the set of states that are reachable with nonzero probability from the initial state, and before the deadline expires. We then encode this information as a Markov decision process to be analyzed with Prism. We apply this technique to compute the minimal probability of a leader being elected before a deadline, for different deadlines, and study how this minimal probability is influenced by using a biased coin and considering different wire lengths.
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 17 (7 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
Weak Bisimulation for Probabilistic Timed Automata
 PROC. OF SEFM’03, IEEE CS
, 2003
"... We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown t ..."
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Cited by 16 (6 self)
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We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown to be preserved when either time, or probability are abstracted away. As an application, we use weak bisimulation for Probabilistic Timed Automata to model and analyze a timing attack on the dining cryptographers protocol.