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232
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
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 171 (41 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.
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.
Approximate symbolic model checking of continuoustime Markov chains (Extended Abstract)
, 1999
"... . This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel operator to express steadystate probabilities. We show that t ..."
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Cited by 137 (24 self)
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. This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel 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 steady stateoperator) and a Volterra integral equation system for timebounded until. We propose a symbolic approximate method for solving the integrals using MTDDs (multiterminal decision diagrams), a generalisation of MTBDDs. These new structures are suitable for numerical integration using quadrature formulas based on equallyspaced abscissas, like trapezoidal, Simpson and Romberg integration schemes. 1 Introduction The mechanised verification of a given (usually) finitestate model against a property expressed in some temporal logic is known as model checking. For probabilistic...
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
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Cited by 88 (32 self)
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Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1
Secure Information Flow by SelfComposition
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... Information flow policies are confidentiality policies that control information leakage through program execution. A common means to enforce secure information flow is through information flow type systems. Although type systems are compositional and usually enjoy decidable type checking or inferenc ..."
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Cited by 86 (11 self)
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Information flow policies are confidentiality policies that control information leakage through program execution. A common means to enforce secure information flow is through information flow type systems. Although type systems are compositional and usually enjoy decidable type checking or inference, their extensibility is very poor: type systems need to be redefined and proven sound for each new single variation of security policy and programming language for which secure information flow verification is desired. In contrast, program logics offer a general mechanism to enforce a variety of safety policies, and for this reason are favored in Proof Carrying Code, a promising security architecture for mobile code. However, the encoding of information flow policies in program logics is not straightforward, because they refer to a relation between two program executions. The purpose of this paper is to investigate logical formulations of secure information flow based on the idea of selfcomposition, that reduces the problem of secure information flow of a program P to a safety property for a program ˆP derived from P, by composing P with a renaming of itself. Selfcomposition enables the use of standard techniques for information flow policies verification, such as program logics and model checking, suitable in Proof Carrying Code infrastructures. We illustrate the applicability of selfcomposition in several settings, including different security policies such as noninterference and controlled forms of declassification, and programming languages such as an imperative language with parallel composition, a nondeterministic language, and finally a language with shared mutable data structures.
Symbolic model checking for probabilistic processes
 IN PROCEEDINGS OF ICALP '97
, 1997
"... We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a stat ..."
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Cited by 85 (30 self)
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We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by MultiTerminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas and MTBDDs to represent Markov chains, and is efficient because it avoids explicit state space construction. A PCTL model checker is being implemented in Verus [9].
Probabilistic Extensions of Process Algebras
 Handbook of Process Algebra
, 2001
"... INTRODUCTION Classic process, algebras such as CCS, CSP and ACP, are wellestablished techniques for modelling and reasoning about functional aspects of concurrent processes. The motivation for studying probabilistic extensions of process algebras is to develop techniques dealing with nonfunctiona ..."
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Cited by 71 (5 self)
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INTRODUCTION Classic process, algebras such as CCS, CSP and ACP, are wellestablished techniques for modelling and reasoning about functional aspects of concurrent processes. The motivation for studying probabilistic extensions of process algebras is to develop techniques dealing with nonfunctional aspects of process behavior, such as performance and reliability. We may want to investigate, e.g., the average response time of a system, or the ? This chapter is dedicated to the fond memory of Linda Christoff. probability that a certain failure occurs. An analysis of these and similar properties requires that some form of information about the stochastic distribution over the occurrence of relevant events is put into the model. For instance, performance evaluation is often based on modeling a system as a continuoustime Markov process, in which distributions over delays between actions and over the choice between different actions are specified. Similar
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 67 (12 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
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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