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Performance analysis of probabilistic timed automata using digital clocks
 Proc. Formal Modeling and Analysis of Timed Systems (FORMATS’03), volume 2791 of LNCS
, 2003
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Symbolic Model Checking of Probabilistic Timed Automata Using Backwards Reachability
, 2000
"... We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system makin ..."
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Cited by 49 (18 self)
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We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling faulttolerance and probabilistic failures. We present a symbolic model checking algorithm for the existential fragment of the logic PTCTL of [13] based on backward reachability as in [12]. The logic allows us to specify properties such as \with probability 0.99 or greater, it is possible to correctly deliver a data packet within 5 time units", or \with probability 0.87 or greater, the system never enters an error state".
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.
Verifying Randomized Byzantine Agreement
 Proc. Formal Techniques for Networked and Distributed Systems (FORTE’02), volume 2529 of LNCS
, 2002
"... Distributed systems increasingly rely on faulttolerant and secure authorization services. An essential primitive used to implement such services is the Byzantine agreement protocol for achieving agreement among n parties even if t parties (t < n=3) are corrupt and behave maliciously. We describ ..."
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Cited by 17 (7 self)
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Distributed systems increasingly rely on faulttolerant and secure authorization services. An essential primitive used to implement such services is the Byzantine agreement protocol for achieving agreement among n parties even if t parties (t < n=3) are corrupt and behave maliciously. We describe our experience verifying the randomized protocol ABBA (Asynchronous Binary Byzantine Agreement) of Cachin, Kursawe and Shoup [5], a practical protocol that incorporates modern thresholdcryptographic techniques and forms a core of powerful asynchronous broadcast protocols [4]. The protocol is ecient (runs in constant expected time), optimal (it tolerates the maximum number of corrupted parties) and provably secure (in the random oracle model). We model the protocol in Cadence SMV, replacing the coin tosses with nondeterministic choice, and provide a proof of the protocol correctness for all n under the assumption that the cryptographic primitives are correct.
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 9 (1 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
PCTL model checking of symbolic probabilistic systems
, 2003
"... Probabilistic model checking is a method for automatically verifying that a probabilistic system satisfies a property with a given likelihood, with the probabilistic temporal logic Pctl being a common choice for the property specification language. In this paper, we explore methods for model che ..."
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Cited by 1 (0 self)
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Probabilistic model checking is a method for automatically verifying that a probabilistic system satisfies a property with a given likelihood, with the probabilistic temporal logic Pctl being a common choice for the property specification language. In this paper, we explore methods for model checking Pctl properties of infinitestate systems in which probabilistic and nondeterministic behaviour coexist. Building on previous work on computing the maximum probability with which a state set is reached in such systems, we utilize symbolic operations on the state sets to generate a finitestate version of the system on which the Pctl model checking problem can be answered. As in the nonprobabilistic case, our model checking algorithm is semidecidable for infinitestate systems. We illustrate our technique using the formalism of probabilistic timed automata, for which previous Pctl model checking techniques were based on an unnecessarily ne subdivisions of the state space.
Timed Automata for the Development of RealTime Systems
, 2011
"... Timed automata are a popular formalism to model realtime systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of realtime ..."
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Cited by 1 (0 self)
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Timed automata are a popular formalism to model realtime systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of realtime system. This paper presents a fairly comprehensive survey, comprised of eighty variants of timed automata. The paper classifies all these eighty variants of timed automata in an effort to determine current developments. It uses analysis techniques, formal properties, and decision problems to draw distinctions between different versions. Moreover, the paper discusses the challenges behind using a timed automata specification to derive an implementation of a working realtime system and presents some solutions. Finally, the paper lists and classifies forty tools supporting timed automata. The paper does not only discuss many variants and their supporting concepts (e.g., closure properties, decision problems), techniques (e.g., for analysis), and tools, but it also attempts to help the reader navigate the vast literature in the field, to highlight differences and similarities between variants, and to reveal research trends and promising avenues for future exploration.
Symbolic Computation of Minimal Probabilistic Reachability
, 2003
"... ... systems featuring both nondeterministic and probabilistic choice. In an earlier paper we de ned symbolic probabilistic systems, an extension of the framework of symbolic transition systems due to Henzinger et. al., and considered the problem of deciding the maximal probability of reaching a ..."
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... systems featuring both nondeterministic and probabilistic choice. In an earlier paper we de ned symbolic probabilistic systems, an extension of the framework of symbolic transition systems due to Henzinger et. al., and considered the problem of deciding the maximal probability of reaching a set of target states. A symbolic probabilistic system is an in nitestate system equipped with an algebra of symbolic operators on its state space, additionally extended with a symbolic encoding of probabilistic transitions to obtain a model for in nitestate probabilistic systems. In this paper we generalise the notion of symbolic probabilistic systems and consider the minimal reachability problem, that is, the problem of computing the minimal probability of reaching a given set of target states. An exact answer to this problem is obtained algorithmically via iteration of a re ned version of the classical predecessor operation, combined with intersection and set dierence operations. As in the previous work on symbolic transition systems, our state space exploration algorithm is semidecidable for in nitestate systems. Together with the earlier work concerning the maximal reachability problem, the results presented here yield a semidecidable algorithm for model checking symbolic systems against the probabilistic temporal logic PCTL. We illustrate our approach with the help of probabilistic timed automata, for which previous veri cation techniques suffered from an unnecessarily ne subdivisions of the state space, or which returned only estimates of the actual probabilities.