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235
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 107 (25 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
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
 IN STACS
, 2005
"... We define Recursive Markov Chains (RMCs), a class of finitely presented denumerable Markov chains, and we study algorithms for their analysis. Informally, an RMC consists of a collection of finitestate Markov chains with the ability to invoke each other in a potentially recursive manner. RMCs offer ..."
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Cited by 95 (13 self)
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We define Recursive Markov Chains (RMCs), a class of finitely presented denumerable Markov chains, and we study algorithms for their analysis. Informally, an RMC consists of a collection of finitestate Markov chains with the ability to invoke each other in a potentially recursive manner. RMCs offer a natural abstract model for probabilistic programs with procedures. They generalize, in a precise sense, a number of well studied stochastic models, including Stochastic ContextFree Grammars (SCFG) and MultiType Branching Processes (MTBP). We focus on algorithms for reachability and termination analysis for RMCs: what is the probability that an RMC started from a given state reaches another target state, or that it terminates? These probabilities are in general irrational, and they arise as (least) fixed point solutions to certain (monotone) systems of nonlinear equations associated with RMCs. We address both the qualitative problem of determining whether the probabilities are 0, 1 or inbetween, and
Petri nets for systems and synthetic biology.
 Formal Methods for Computational Systems Biology, Lecture Notes in Computer Science,
, 2008
"... Abstract. We give a description of a Petri netbased framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, b ..."
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Cited by 80 (23 self)
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Abstract. We give a description of a Petri netbased framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks. Motivation Biochemical reaction systems have by their very nature three distinctive characteristics. (1) They are inherently bipartite, i.e. they consist of two types of game players, the species and their interactions. (2) They are inherently concurrent, i.e. several interactions can usually happen independently and in parallel. (3) They are inherently stochastic, i.e. the timing behaviour of the interactions is governed by stochastic laws. So it seems to be a natural choice to model and analyse them with a formal method, which shares exactly these distinctive characteristics: stochastic Petri nets. However, due to the computational efforts required to analyse stochastic models, two abstractions are more popular: qualitative models, abstracting away from any time dependencies, and continuous models, commonly used to approximate stochastic behaviour by a deterministic one. We describe an overall framework to unify these three paradigms, providing a family of related models with high analytical power. The advantages of using Petri nets as a kind of umbrella formalism are seen in the following: M. Bernardo, P. Degano, and G. Zavattaro (Eds.): SFM
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.
Comparative branchingtime semantics for Markov chains
 Information and Computation
, 2003
"... This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilisti ..."
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Cited by 64 (17 self)
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This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branchingtime relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and preorders in the continuous and discretetime setting. The results are summarized in a branchingtime spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship. Key Words: comparative semantics, Markov chain, (weak) simulation, (weak) bisimulation, temporal logic
Efficient computation of timebounded reachability probabilities in uniform continuoustime Markov decision processes
, 2004
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A Bayesian Approach to Model Checking Biological Systems ⋆
"... Abstract. Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been sh ..."
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Cited by 52 (15 self)
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Abstract. Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequential Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Model Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requiring fewer system simulations. Another advantage of our approach is the ability to incorporate prior Biological knowledge about the model being verified. We demonstrate our algorithm on a variety of models from the Systems Biology literature and show that it enables faster verification than stateoftheart techniques, even when no prior knowledge is available. 1
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 49 (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.
Bayesian Statistical Model Checking with Application to Stateflow/Simulink Verification
, 2010
"... We address the problem of model checking stochastic systems, i.e. checking whether a stochastic system satisfies a certain temporal property with a probability greater (or smaller) than a fixed threshold. In particular, we present a novel Statistical Model Checking (SMC) approach based on Bayesian s ..."
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Cited by 46 (9 self)
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We address the problem of model checking stochastic systems, i.e. checking whether a stochastic system satisfies a certain temporal property with a probability greater (or smaller) than a fixed threshold. In particular, we present a novel Statistical Model Checking (SMC) approach based on Bayesian statistics. We show that our approach is feasible for hybrid systems with stochastic transitions, a generalization of Simulink/Stateflow models. Standard approaches to stochastic (discrete) systems require numerical solutions for large optimization problems and quickly become infeasible with larger state spaces. Generalizations of these techniques to hybrid systems with stochastic effects are even more challenging. The SMC approach was pioneered by Younes and Simmons in the discrete and nonBayesian case. It solves the verification problem by combining randomized sampling of system traces (which is very efficient for Simulink/Stateflow) with hypothesis testing or estimation. We believe SMC is essential for scaling up to large Stateflow/Simulink models. While the answer to the verification problem is not guaranteed to be correct, we prove that Bayesian SMC can make the probability of giving a wrong answer arbitrarily small. The advantage is that answers can usually be obtained much faster than with standard, exhaustive model checking
2007): Bisimulation Minimisation Mostly Speeds Up Probabilistic Model Checking
 In: Tools and Algorithms for the Construction and Analysis of Systems, 13th International Conference (TACAS’07), Lecture Notes in Computer Science 4424
"... The following full text is a publisher's version. ..."
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Cited by 40 (9 self)
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The following full text is a publisher's version.