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25
Verification by abstract interpretation
 In Verification: Theory and Practice
, 2003
"... Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is ..."
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Cited by 237 (16 self)
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Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is illustrated on the particular cases of predicate abstraction, which is revisited to handle infinitary abstractions, and on the new parametric predicate abstraction. 1
CSL model checking of biochemical networks with interval decision diagrams
 in Proc. CMSB 2009. LNCS/LNBI 5688
, 2009
"... Abstract. This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrixvector and vectormatrix multiplication are the major tasks of exact analysis. We introduce a simple, but po ..."
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Cited by 12 (7 self)
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Abstract. This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrixvector and vectormatrix multiplication are the major tasks of exact analysis. We introduce a simple, but powerful algorithm which uses explicitly the Petri net structure and allows for parallelisation. We present results demonstrating the efficiency of our first prototype implementation when applied to biochemical network models, specifically with increasing token numbers. Our tool currently supports CSL model checking of timebounded operators and the Next operator for ordinary stochastic Petri nets. 1
On the connections between PCTL and dynamic programming
 Proceedings of the 13th ACM international conference on Hybrid Systems: Computation and Control
"... ABSTRACT. Probabilistic Computation Tree Logic (PCTL) is a wellknown modal logic which has become a standard for expressing temporal properties of finitestate Markov chains in the context of automated model checking. In this paper, we give a definition of PCTL for noncountablespace Markov chains, ..."
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Cited by 9 (0 self)
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ABSTRACT. Probabilistic Computation Tree Logic (PCTL) is a wellknown modal logic which has become a standard for expressing temporal properties of finitestate Markov chains in the context of automated model checking. In this paper, we give a definition of PCTL for noncountablespace Markov chains, and we show that there is a substantial affinity between certain of its operators and problems of Dynamic Programming. After proving some uniqueness properties of the solutions to the latter, we conclude the paper with two examples to show that some recovery strategies in practical applications, which are naturally stated as reachavoid problems, can be actually viewed as particular cases of PCTL formulas. 1.
Biomodel Engineering – From Structure to Behavior
"... Abstract. Biomodel engineering is the science of designing, constructing and analyzing computational models of biological systems. It forms a systematic and powerful extension of earlier mathematical modeling approaches and has recently gained popularity in systems biology and synthetic biology. In ..."
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Cited by 7 (3 self)
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Abstract. Biomodel engineering is the science of designing, constructing and analyzing computational models of biological systems. It forms a systematic and powerful extension of earlier mathematical modeling approaches and has recently gained popularity in systems biology and synthetic biology. In this brief review for systems biologists and computational modelers, we introduce some of the basic concepts of successful biomodel engineering, illustrating them with examples from a variety of application domains, ranging from metabolic networks to cellular signaling cascades. We also present a more detailed outline of one of the major techniques of biomodel engineering – Petri net models – which provides a flexible and powerful tool for building, validating and exploring computational descriptions of biological systems.
Approximate probabilistic analysis of biopathway dynamics
 Bioinformatics
, 2012
"... Motivation: Biopathways are often modeled as systems of ordinary differential equations (ODEs). Such systems will usually have many unknown parameters and hence will be difficult to calibrate. Since the data available for calibration will have limited precision, an approximate representation of the ..."
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Motivation: Biopathways are often modeled as systems of ordinary differential equations (ODEs). Such systems will usually have many unknown parameters and hence will be difficult to calibrate. Since the data available for calibration will have limited precision, an approximate representation of the ODEs dynamics should suffice. One must however be able to efficiently construct such approximations for large models and perform model calibration and subsequent analysis. Results: We present a GPUbased scheme by which a system of ODEs is approximated as a dynamic Bayesian network (DBN). We then construct a model checking procedure for DBNs based on a simple probabilistic linear time temporal logic. The GPU implementation considerably extends the reach of our previous PCcluster based implementation (Liu et al., 2011b). Further, the key components of our algorithm can serve as the GPU kernel for other Monte Carlo simulations based analysis of biopathway dynamics. Similarly, our model checking framework is a generic one and can be applied in other systems biology settings. We have tested our methods on three ODE models of biopathways: the EGFNGF pathway, the segmentation clock network and the MLCphosphorylation pathway models. The GPU implementation shows significant gains in performance and scalability while the model checking framework turns out to be convenient and efficient for specifying and verifying interesting pathways properties. Availability: The source code is freely available at
A comparative study of stochastic analysis techniques
 In Proc. CMSB 2010
, 2010
"... Stochastic models are becoming increasingly popular in Systems Biology. They are compulsory, if the stochastic noise is crucial for the behavioural properties to be investigated. Thus, substantial effort has been made to develop appropriate and efficient stochastic analysis techniques. The impres ..."
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Cited by 6 (5 self)
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Stochastic models are becoming increasingly popular in Systems Biology. They are compulsory, if the stochastic noise is crucial for the behavioural properties to be investigated. Thus, substantial effort has been made to develop appropriate and efficient stochastic analysis techniques. The impressive progress of hardware power and specifically the advent of multicore computers have ameliorated the computational tractability of stochastic models. We report on a comparative study focusing on the three base case techniques of stochastic analysis: exact numerical analysis, approximative numerical analysis, and simulation. For modelling we use extended stochastic Petri nets, which allows us to take advantage of structural information and to complement the stochastic analyses by qualitative analyses, belonging to the standard body of Petri net theory. 1.
Approximate model checking of PCTL involving unbounded path properties,” ICFEM’09
, 2009
"... Abstract. We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with statespace explosion that makes the exact model checking by numeri ..."
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Cited by 2 (0 self)
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Abstract. We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with statespace explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties; or rely on userspecified finite bound on the sample path length. We propose a new method that does not have such restrictions and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for a suitably chosen value of the bound. In essence, our method is a twophase process: (a) the first phase is concerned with identifying the bound k0; (b) the second phase computes the probability of satisfying the k0bounded until property as an estimate for the probability of satisfying the corresponding unbounded until property. In both phases, it is sufficient to verify bounded until properties which can be effectively done using existing statistical techniques. We prove the correctness of our technique and present its prototype implementations. We empirically show the practical applicability of our method by considering different case studies including a simple infinitestate model, and large finitestate models such as IPv4 zeroconf protocol and dining philosopher protocol modeled as Discrete Time Markov chains. 1
Y.: Symbolic approximation of the bounded reachability probability in large Markov chains
, 2014
"... Abstract. We present a novel technique to analyze the bounded reachability probability problem for large Markov chains. The essential idea is to incrementally search for sets of paths that lead to the goal region and to choose the sets in a way that allows us to easily determine the probability ma ..."
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Abstract. We present a novel technique to analyze the bounded reachability probability problem for large Markov chains. The essential idea is to incrementally search for sets of paths that lead to the goal region and to choose the sets in a way that allows us to easily determine the probability mass they represent. To effectively analyze the system dynamics using an SMT solver, we employ a finiteprecision abstraction on the Markov chain and a custom quantifier elimination strategy. Through experimental evaluation on PRISM benchmark models we demonstrate the feasibility of the approach on models that are out of reach for previous methods. 1
Systems biology Advance Access publication November 29, 2011 Gaussian process modelling for bicoid mRNA regulation in spatiotemporal Bicoid profile
, 2011
"... Motivation: Bicoid protein molecules, translated from maternally provided bicoid mRNA, establish a concentration gradient in Drosophila early embryonic development. There is experimental evidence that the synthesis and subsequent destruction of this protein is regulated at source by precise control ..."
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Motivation: Bicoid protein molecules, translated from maternally provided bicoid mRNA, establish a concentration gradient in Drosophila early embryonic development. There is experimental evidence that the synthesis and subsequent destruction of this protein is regulated at source by precise control of the stability of the maternal mRNA. Can we infer the driving function at the source from noisy observations of the spatiotemporal protein profile? We use nonparametric Gaussian process regression for modelling the propagation of Bicoid in the embryo and infer aspects of source regulation as a posterior function. Results: With synthetic data from a 1D diffusion model with a source simulated to model mRNA stability regulation, our results establish that the Gaussian process method can accurately infer the driving function and capture the spatiotemporal dynamics of embryonic Bicoid propagation. On real data from the FlyEx database, too, the reconstructed source function is indicative of stability regulation, but is temporally smoother than what we expected, partly due to the fact that the dataset is only partially observed. To be in line with recent thinking on the subject, we also analyse this model with a spatial gradient of maternal mRNA, rather than being fixed at only the anterior pole.
Graph transforms for modeling chemical reaction pathways
"... ABSTRACT In this paper we discuss some general graphtheoretic formalism analogous to the chemical concepts of reactions and kits of reaction rules. We believe that this mathematical formalism may lead to improvements in Computerassisted Organic Synthesis. Further we indicate that hypergraphs and ..."
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ABSTRACT In this paper we discuss some general graphtheoretic formalism analogous to the chemical concepts of reactions and kits of reaction rules. We believe that this mathematical formalism may lead to improvements in Computerassisted Organic Synthesis. Further we indicate that hypergraphs and its structure can be used to model the chemical reaction network.