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107
Probabilistic model checking of complex biological pathways
, 2006
"... Abstract. Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicab ..."
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Cited by 94 (18 self)
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Abstract. Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. 1
BioPEPA: a framework for the modelling and analysis of biological systems
, 2008
"... In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use ..."
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Cited by 94 (25 self)
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In this work we present BioPEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. The domain of application is the one of biochemical networks. BioPEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. BioPEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered. Finally, we show the translation of three biological models into the new language and we report some analysis results.
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.
A Logical Characterization of Bisimulation for Labeled Markov Processes
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [5]. ffl Bisimulation can be characterized by a very weakmodal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be charac ..."
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Cited by 41 (11 self)
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This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [5]. ffl Bisimulation can be characterized by a very weakmodal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper and there are surely many more. ffl We do not need any finite branching assumption yetthere is no need of infinitary conjunction. ffl We give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.
Automated Verification Techniques for Probabilistic Systems
"... Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to ..."
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Cited by 40 (16 self)
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Abstract. This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost or rewardbased measures. We also discuss multiobjective probabilistic model checking, used to analyse tradeoffs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multicomponent probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial. 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).
An Operational Semantics for Probabilistic Concurrent Constraint Programming
, 1998
"... This paper investigates a probabilistic version of the concurrent constraint programming paradigm (CCP). The aim is to introduce the possibility to formulate so called "randomised algorithms" within the CCP framework. Differently from common approaches in (imperative) highlevel programmin ..."
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Cited by 32 (12 self)
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This paper investigates a probabilistic version of the concurrent constraint programming paradigm (CCP). The aim is to introduce the possibility to formulate so called "randomised algorithms" within the CCP framework. Differently from common approaches in (imperative) highlevel programming languages, which rely on some kind of random() function, we introduce randomness in the very definition of the language by means of a probabilistic choice construct. This allows a program to make stochastic moves during its execution. We call the resulting language Probabilistic Concurrent Constraint Programming (PCCP). We present an operational semantics for PCCP by means of a probabilistic transition system such that the execution of a PCCP program may be seen as a stochastic process, i.e. as a random walk on the transition graph. The transition probabilities are given explicitly. This semantics captures a notion of observables which combines results of computations and the probability of those re...
Probabilistic Reachability for Parametric Markov Models
"... Given a parametric Markov model, we consider the problem of computing the formula expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is compute ..."
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Cited by 29 (4 self)
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Given a parametric Markov model, we consider the problem of computing the formula expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form expression representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in an exponential growth of the regular expression relative to the number of states. We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids the exponential blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with nondeterminism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on nontrivial models.
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.
Scalable Differential Analysis of Process Algebra Models
"... The exact performance analysis of largescale software systems with discretestate approaches is difficult because of the wellknown problem of statespace explosion. This paper considers this problem with regard to the stochastic process algebra PEPA, presenting a deterministic approximation to the ..."
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Cited by 24 (8 self)
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The exact performance analysis of largescale software systems with discretestate approaches is difficult because of the wellknown problem of statespace explosion. This paper considers this problem with regard to the stochastic process algebra PEPA, presenting a deterministic approximation to the underlying Markov chain model based on ordinary differential equations. The accuracy of the approximation is assessed by means of a substantial case study of a distributed multithreaded application.