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236
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
 International Journal on Software Tools for Technology Transfer (STTT
, 2002
"... In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and ..."
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Cited by 201 (32 self)
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In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking speci cations in the probabilistic temporal logics PCTL and CSL. Motivated by the success of model checkers such as SMV, which use BDDs (binary decision diagrams), we have developed an implementation of PCTL and CSL model checking based on MTBDDs (multiterminal BDDs) and BDDs. Existing work in this direction has been hindered by the generally poor performance of MTBDDbased numerical computation, which is often substantially slower than explicit methods using sparse matrices. We present a novel hybrid technique which combines aspects of symbolic and explicit approaches to overcome these performance problems. For typical examples, we achieve orders of magnitude speedup compared to MTBDDs and are able to almost match the speed of sparse matrices whilst maintaining considerable space savings.
Anonymity and Information Hiding in Multiagent Systems
, 2003
"... We provide a framework for reasoning about informationhiding requirements in multiagent systems and for reasoning about anonymity in particular. Our framework employs the modal logic of knowledge within the context of the runs and systems framework, much in the spirit of our earlier work on secrecy ..."
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Cited by 97 (2 self)
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We provide a framework for reasoning about informationhiding requirements in multiagent systems and for reasoning about anonymity in particular. Our framework employs the modal logic of knowledge within the context of the runs and systems framework, much in the spirit of our earlier work on secrecy [9]. We give several definitions of anonymity with respect to agents, actions, and observers in multiagent systems, and we relate our definitions of anonymity to other definitions of information hiding, such as secrecy. We also give probabilistic definitions of anonymity that are able to quantify an observer's uncertainty about the state of the system. Finally, we relate our definitions of anonymity to other formalizations of anonymity and information hiding, including definitions of anonymity in the process algebra CSP and definitions of information hiding using function views.
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 84 (27 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".
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 79 (12 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.
Performance analysis of probabilistic timed automata using digital clocks
 Proc. Formal Modeling and Analysis of Timed Systems (FORMATS’03), volume 2791 of LNCS
, 2003
"... ..."
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.
Monte Carlo Model Checking
 In Proc. of Tools and Algorithms for Construction and Analysis of Systems (TACAS 2005), volume 3440 of LNCS
, 2005
"... Abstract. We present MC 2, what we believe to be the first randomized, Monte Carlo algorithm for temporallogic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification. Given a specification S of a finitestate system, a ..."
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Cited by 59 (4 self)
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Abstract. We present MC 2, what we believe to be the first randomized, Monte Carlo algorithm for temporallogic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification. Given a specification S of a finitestate system, an LTL (Linear Temporal Logic) formula ϕ, and parameters ɛ and δ, MC 2 takes N = ln(δ) / ln(1 − ɛ) random samples (random walks ending in a cycle, i.e lassos) from the Büchi automaton B = BS × B¬ϕ to decide if L(B) = ∅. Should a sample reveal an accepting lasso l, MC 2 returns false with l as a witness. Otherwise, it returns true and reports that with probability less than δ, pZ < ɛ, where pZ is the expectation of an accepting lasso in B. It does so in time O(N · D) and space O(D), where D is B’s recurrence diameter, using a number of samples N that is optimal to within a constant factor. Our experimental results demonstrate that MC 2 is fast, memoryefficient, and scales very well.
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 58 (6 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.
Weak probabilistic anonymity
 INRIA FUTURS AND LIX
, 2005
"... Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. In this paper we propose a notion of weak probabilistic anonymity, where weak refers to the fact ..."
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Cited by 49 (11 self)
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Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. In this paper we propose a notion of weak probabilistic anonymity, where weak refers to the fact that some amount of probabilistic information may be revealed by the protocol. This information can be used by an observer to infer the likeliness that the action has been performed by a certain user. The aim of this work is to study the degree of anonymity that the protocol can still ensure, despite the leakage of information. We illustrate our ideas by using the example of the dining cryptographers with biased coins. We consider both the cases of nondeterministic and probabilistic users. Correspondingly, we propose two notions of weak anonymity and we investigate their respective dependencies on the biased factor of the coins.
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 48 (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