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PRISM: Probabilistic symbolic model checker
, 2002
"... Abstract. In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports two probabilistic models: continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking such systems ..."
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Cited by 205 (15 self)
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Abstract. In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports two probabilistic models: continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking such systems against specifications written in the probabilistic temporal logics PCTL and CSL. The tool features three model checking engines: one symbolic, using BDDs (binary decision diagrams) and MTBDDs (multiterminal BDDs); one based on sparse matrices; and one which combines both symbolic and sparse matrix methods. PRISM has been successfully used to analyse probabilistic termination, performance, dependability and quality of service properties for a range of systems, including randomized distributed algorithms, polling systems, workstation cluster and wireless cell communication. 1
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 157 (31 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.
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 59 (10 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 51 (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.
Faster and Symbolic CTMC Model Checking
, 2001
"... This paper reports on the implementation and the experiments with symbolic model checking of continuoustime Markov chains using multiterminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient ..."
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Cited by 46 (21 self)
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This paper reports on the implementation and the experiments with symbolic model checking of continuoustime Markov chains using multiterminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steadystate performance measures.
PRISM: Probabilistic Model Checking for Performance and Reliability Analysis
 ACM SIGMETRICS Performance Evaluation Review
"... Probabilistic model checking is a formal verification technique for the modelling and analysis of stochastic systems. It has proved to be useful for studying a wide range of quantitative properties of models taken from many different application domains. This includes, for example, performance and r ..."
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Cited by 30 (1 self)
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Probabilistic model checking is a formal verification technique for the modelling and analysis of stochastic systems. It has proved to be useful for studying a wide range of quantitative properties of models taken from many different application domains. This includes, for example, performance and reliability properties of computer and communication systems. In this paper, we give an overview of the probabilistic model checking tool PRISM, focusing in particular on its support for continuoustime Markov chains and Markov reward models, and how these can be used to analyse performability properties. 1.
Policy iteration for decentralized control of Markov decision processes
 JAIR
"... Coordination of distributed agents is required for problems arising in many areas, including multirobot systems, networking and ecommerce. As a formal framework for such problems, we use the decentralized partially observable Markov decision process (DECPOMDP). Though much work has been done on o ..."
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Cited by 22 (15 self)
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Coordination of distributed agents is required for problems arising in many areas, including multirobot systems, networking and ecommerce. As a formal framework for such problems, we use the decentralized partially observable Markov decision process (DECPOMDP). Though much work has been done on optimal dynamic programming algorithms for the singleagent version of the problem, optimal algorithms for the multiagent case have been elusive. The main contribution of this paper is an optimal policy iteration algorithm for solving DECPOMDPs. The algorithm uses stochastic finitestate controllers to represent policies. The solution can include a correlation device, which allows agents to correlate their actions without communicating. This approach alternates between expanding the controller and performing valuepreserving transformations, which modify the controller without sacrificing value. We present two efficient valuepreserving transformations: one can reduce the size of the controller and the other can improve its value while keeping the size fixed. Empirical results demonstrate the usefulness of valuepreserving transformations in increasing value while keeping controller size to a minimum. To broaden the applicability of the approach, we also present a heuristic version of the policy iteration algorithm, which sacrifices convergence to optimality. This algorithm further reduces the size of the controllers at each step by assuming that probability distributions over the other agents’ actions are known. While this assumption may not hold in general, it helps produce higher quality solutions in our test problems. 1.
Symbolic Representations and Analysis of Large Probabilistic Systems
 In Validation of Stochastic Systems
, 2004
"... Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the stat ..."
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Cited by 16 (2 self)
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Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the state spaces which can be tackled. In general, this is done by using data structures which provide compact storage but which are still efficient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multivalued decision diagrams (MDDs), multiterminal binary decision diagrams (MTBDDs) and matrix diagrams. 1
A Symbolic OutofCore Solution Method for Markov Models
 In Proc. Workshop on Parallel and Distributed Model Checking (PDMC'02), volume 68.4 of Electronic Notes in Theoretical Computer Science
, 2002
"... Despite considerable eort, the statespace explosion problem remains an issue in the analysis of Markov models. Given structure, symbolic representations can result in very compact encoding of the models. However, a major obstacle for symbolic methods is the need to store the probability vector(s) e ..."
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Cited by 14 (11 self)
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Despite considerable eort, the statespace explosion problem remains an issue in the analysis of Markov models. Given structure, symbolic representations can result in very compact encoding of the models. However, a major obstacle for symbolic methods is the need to store the probability vector(s) explicitly in main memory. In this paper, we present a novel algorithm which relaxes these memory limitations by storing the probability vector on disk. The algorithm has been implemented using an MTBDDbased data structure to store the matrix and an array to store the vector. We report on experimental results for two benchmark models, a Kanban manufacturing system and a exible manufacturing system, with models as large as 133 million states.
An overview of competitive and adversarial approaches to designing dynamic power management strategies
 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
, 2005
"... Dynamic power management (DPM) refers to the problem of judicious application of various lowpower techniques based on runtime conditions in an embedded system to minimize the total energy consumption. To be effective, often such decisions take into account the operating conditions and the systeml ..."
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Cited by 13 (0 self)
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Dynamic power management (DPM) refers to the problem of judicious application of various lowpower techniques based on runtime conditions in an embedded system to minimize the total energy consumption. To be effective, often such decisions take into account the operating conditions and the systemlevel design goals. DPM has been a subject of intense research in the past decade driven by the need for low power consumption in modern embedded devices. We present a comprehensive overview of two closely related approaches to designing DPM strategies, namely, competitive analysis approach and model checking approach based on adversarial modeling. Although many other approaches exist for solving the systemlevel DPM problem, these two approaches are closely related and are based on a common theme. This commonality is in the fact that the underlying model is that of a competition between the system and an adversary. The environment that puts service demands on devices is viewed as an adversary, or to be in competition with the system to make it burn more energy, and the DPM strategy is employed by the system to counter that.