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PRISM 4.0: Verification of Probabilistic Realtime Systems
"... Abstract. This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and realtime characteristics. In many application do ..."
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Cited by 236 (45 self)
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Abstract. This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and realtime characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is opensource, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicitstate probabilistic model checking library; a discreteevent simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite. 1
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
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
A unifying framework for modelling and analysing biochemical pathways using Petri nets
 TR I02, CS DEP., BTU COTTBUS
, 2007
"... 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 comple ..."
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Cited by 59 (24 self)
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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. A key contribution of the paper consists in a precise definition of biochemically interpreted stochastic Petri nets. 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.
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
Rulebased modeling of biochemical systems with BioNetGen
 IN METHODS IN MOLECULAR BIOLOGY: SYSTEMS BIOLOGY
, 2009
"... Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactio ..."
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Cited by 43 (10 self)
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Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactions into a model for the dynamics of a signaltransduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of proteinprotein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rulebased model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rulebased modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly largescale models for other biochemical systems.
On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology
 In M.Heiner and A.M.Uhrmacher (eds.), CMSB’08: Proc. of the sixth international conference on Computational Methods in Systems Biology
, 2008
"... Abstract. Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeller that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we propose to go one step ..."
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Cited by 37 (4 self)
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Abstract. Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeller that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we propose to go one step further by defining a continuous degree of satisfaction of a temporal logic formula with constraints. We show how such a satisfaction measure can be used as a fitness function with stateoftheart search methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade. 1
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).
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.
Formal Cell Biology in Biocham
"... Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these ..."
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Cited by 16 (6 self)
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Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these graphs with formal methods originating from programming theory. We consider systems of biochemical reactions with kinetic expressions, as written in the Systems Biology Markup Language (SBML), and interpreted in the Biochemical Abstract Machine (Biocham) at different levels of abstraction, by either an asynchronous boolean transition system, a continuous time Markov chain, or a system of Ordinary Differential Equations over molecular concentrations. We show that under general conditions satisfied in practice, the activation/inhibition graph is independent of the precise kinetic expressions, and is computable in linear time in the number of reactions. Then we consider the formalization of the biological properties of systems, as observed in experiments, in temporal logics. We show that these logics are expressive enough to capture semiqualitative semiquantitative properties of the boolean and differential semantics of reaction models, and that modelchecking techniques can be used to validate a model w.r.t. its temporal specification, complete it, and search for kinetic parameter values. We illustrate this modelling method with examples on the MAPK signalling cascade, and on Kohn’s map of the mammalian cell cycle. 1