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20
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 59 (11 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
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 55 (6 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
D.: Symmetry reduction for probabilistic model checking
 International Organization for Standardization. ISO Information Processing Systems  Data Communication HighLevel Data Link Control Procedure  Frame Structure. IS 3309
, 2006
"... Abstract. We present an approach for applying symmetry reduction techniques to probabilistic model checking, a formal verification method for the quantitative analysis of systems with stochastic characteristics. We target systems with a set of nontrivial, but interchangeable, components such as tho ..."
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Cited by 22 (7 self)
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Abstract. We present an approach for applying symmetry reduction techniques to probabilistic model checking, a formal verification method for the quantitative analysis of systems with stochastic characteristics. We target systems with a set of nontrivial, but interchangeable, components such as those which commonly arise in randomised distributed algorithms or probabilistic communication protocols. We show, for three types of probabilistic models, that symmetry reduction, similarly to the nonprobabilistic case, allows verification to instead be performed on a bisimilar quotient model which may be up to factorially smaller. We then propose an efficient algorithm for the construction of the quotient model using a symbolic implementation based on multiterminal binary decision diagrams (MTBDDs) and, using four large case studies, demonstrate that this approach offers not only a dramatic increase in the size of probabilistic model which can be quantitatively analysed but also a significant decrease in the corresponding runtimes. 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 14 (6 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).
Model Checking Meets Performance Evaluation
"... Markov chains are one of the most popular models for the evaluation of performance and dependability of information processing systems. To obtain performance measures, typically longrun or transient state probabilities of Markov chains are determined. Sometimes the Markov chain at hand is equipped ..."
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Cited by 5 (1 self)
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Markov chains are one of the most popular models for the evaluation of performance and dependability of information processing systems. To obtain performance measures, typically longrun or transient state probabilities of Markov chains are determined. Sometimes the Markov chain at hand is equipped with rewards and computations involve determining longrun or instantaneous reward probabilities.
Exogenous Probabilistic Computation Tree Logic
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 4 (1 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Eager Markov chains
 In Proc. ATVA ’06, 4Ø�Int. Symp. on Automated Technology for Verification and Analysis
, 2006
"... Abstract. We consider infinitestate discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more thanÒsteps is bounded by some exponentially decreasing function�(Ò). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel ..."
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Cited by 3 (2 self)
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Abstract. We consider infinitestate discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more thanÒsteps is bounded by some exponentially decreasing function�(Ò). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel Systems, Probabilistic Vector Addition Systems with States, and Noisy Turing Machines, and that the bounding function�(Ò) can be effectively constructed for them. Furthermore, we study the problem of computing the expected reward (or cost) of runs until reaching the final states, where rewards are assigned to individual runs by computable reward functions. For eager Markov chains, an effective path exploration scheme, based on forward reachability analysis, can be used to approximate the expected reward upto an arbitrarily small error. 1
Limiting Behavior of Markov Chains with Eager Attractors
, 2006
"... We consider discrete infinitestate Markov chains which contain an eager finite attractor. A finite attractor is a finite subset of states that is eventually reached with probability 1 from every other state, and the eagerness condition requires that the probability of avoiding the attractor in n o ..."
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Cited by 2 (2 self)
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We consider discrete infinitestate Markov chains which contain an eager finite attractor. A finite attractor is a finite subset of states that is eventually reached with probability 1 from every other state, and the eagerness condition requires that the probability of avoiding the attractor in n or more steps after leaving it is exponentially bounded in n. Examples of such Markov chains are those induced by probabilistic lossy channel
Structure and Parameter Estimation for Cell Systems Biology Models
"... In this work we present a new methodology for structure and parameter estimation in cell systems biology modelling. Our modelling framework is based on P systems, an unconventional computational paradigm that abstracts from the structure and functioning of the living cell. The process of designing m ..."
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Cited by 1 (1 self)
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In this work we present a new methodology for structure and parameter estimation in cell systems biology modelling. Our modelling framework is based on P systems, an unconventional computational paradigm that abstracts from the structure and functioning of the living cell. The process of designing models, consisting of both the optimisation of the modular structure and of the stochastic kinetic parameters, is performed using a memetic algorithm. Specifically, we use a nested evolutionary algorithm where the first layer evolves rule structures while the inner layer, implemented also as a genetic algorithm (GA), fine tunes the parameters of the model. Our approach consists of an incremental methodology. Starting from very simple P system modules specifying basic molecular interactions, more complicated modules are produced to model more complex molecular systems. These newly found modules are in turn added to the library of available P systems modules so as to be used subsequently to develop more intricate and circuitous cellular models. The effectiveness of the algorithm was tested on three case studies, namely, molecular complexation, enzymatic reactions and autoregulation in transcriptional networks.
Temporalization of probabilistic propositional logic
, 2008
"... In this paper we study several properties of the Exogenous Probabilistic Propositional Logic (EPPL), a logic for reasoning about probabilities, with the purpose of introducing a temporal version Exogenous Probabilistic Linear Temporal Logic (EPLTL). In detail, we give a small model theorem for EPPL ..."
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Cited by 1 (1 self)
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In this paper we study several properties of the Exogenous Probabilistic Propositional Logic (EPPL), a logic for reasoning about probabilities, with the purpose of introducing a temporal version Exogenous Probabilistic Linear Temporal Logic (EPLTL). In detail, we give a small model theorem for EPPL and introduce a satisfaction and a model checking algorithm for both EPPL and EPLTL. We are also able to provide a (weakly) complete calculus for EPLTL. Finally, we conclude by pointing out some future work. 1