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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
The ins and outs of the probabilistic model checker MRMC
 IN PROC. QEST’09
, 2009
"... The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions. Distinguishing features of MRMC are its support for computing time and rewardbounded reachability probabilities, (prop ..."
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Cited by 75 (18 self)
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The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports PCTL and CSL model checking, and their reward extensions. Distinguishing features of MRMC are its support for computing time and rewardbounded reachability probabilities, (propertydriven) bisimulation minimization, and precise onthefly steadystate detection. Recent tool features include timebounded reachability analysis for uniform CTMDPs and CSL model checking by discreteevent simulation. This paper presents the tool’s current status and its implementation details.
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 59 (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.
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
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 49 (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
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
Ymer: A statistical model checker
 COMPUTER AIDED VERIFICATION. LNCS
, 2005
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Quantitative Verification: Models, Techniques and Tools
, 2007
"... Automated verification is a technique for establishing if certain properties, usually expressed in temporal logic, hold for a system model. The model can be defined using a highlevel formalism or extracted directly from software using methods such as abstract interpretation. The verification procee ..."
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Cited by 35 (15 self)
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Automated verification is a technique for establishing if certain properties, usually expressed in temporal logic, hold for a system model. The model can be defined using a highlevel formalism or extracted directly from software using methods such as abstract interpretation. The verification proceeds through exhaustive exploration of the statetransition graph of the model and is therefore more powerful than testing. Quantitative verification is an analogous technique for establishing quantitative properties of a system model, such as the probability of battery power dropping below minimum, the expected time for message delivery and the expected number of messages lost before protocol termination. Models analysed through this method are typically variants of Markov chains, annotated with costs and rewards that describe resources and their usage during execution. Properties are expressed in temporal logic extended with probabilistic and reward operators. Quantitative verification involves a combination of a traversal of the statetransition graph of the model and numerical computation. This paper gives a brief overview of current research in quantitative verification, concentrating on the potential of the method and outlining future challenges. The modelling approach is described and the usefulness of the methodology illustrated with an example of a realworld protocol standard – Bluetooth device discovery – that has been analysed using the PRISM model checker (www.prismmodelchecker.org).
Statistical model checking: An overview
 RV 2010
, 2010
"... Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical a ..."
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Cited by 29 (6 self)
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Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.
Using Probabilistic Model Checking in Systems Biology
"... Probabilistic model checking is a formal verification framework for systems which exhibit stochastic behaviour. It has been successfully applied to a wide range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we demonstrate i ..."
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Cited by 25 (0 self)
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Probabilistic model checking is a formal verification framework for systems which exhibit stochastic behaviour. It has been successfully applied to a wide range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we demonstrate its applicability to the analysis of biological pathways and show how it can yield a better understanding of the dynamics of these systems. Through a case study of the MAP (MitogenActivated Protein) Kinase cascade, we explain how biological pathways can be modelled in the probabilistic model checker PRISM and how this enables the analysis of a rich selection of quantitative properties. 1.