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Course: M2-6: Abstract interpretation: application to verication and static analysis Note: Other internships are possible on the topic of static analysis, abstract interpretation , and applications to Systems Biology. Please contact the... more
Course: M2-6: Abstract interpretation: application to verication and static analysis Note: Other internships are possible on the topic of static analysis, abstract interpretation , and applications to Systems Biology. Please contact the internship supervisor for more information.
Course: M2-6: Abstract interpretation: application to verication and static analysis Note: Other internships are possible on the topic of static analysis, abstract interpretation , and applications to Systems Biology. Please contact the... more
Course: M2-6: Abstract interpretation: application to verication and static analysis Note: Other internships are possible on the topic of static analysis, abstract interpretation , and applications to Systems Biology. Please contact the internship supervisor for more information.
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Motivation We present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator,... more
Motivation We present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator, the Kappa Static Analyzer and the Kappa Story Extractor. In addition to these components, we describe the Kappa User Interface, which includes a range of interactive visualization tools for rule-based models needed to make sense of the complexity of biological systems. We argue that, in this approach, modeling is akin to programming and can likewise benefit from an integrated development environment. Our platform is a step in this direction. Results We discuss details about the computation and rendering of static, dynamic, and causal views of a model, which include the contact map (CM), snaphots at different resolutions, the dynamic influence network (DIN) and causal compression. We provide use cases illustrating how these concepts generate insight...
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We present an Abstract Interpretation-based framework for automatically analyzing programs containing digital filters. Our framework allows refining existing analyses so that they can handle given classes of digital filters. We only have... more
We present an Abstract Interpretation-based framework for automatically analyzing programs containing digital filters. Our framework allows refining existing analyses so that they can handle given classes of digital filters. We only have to design a class of symbolic properties that describe the invariants throughout filter iterations, and to describe how these properties are transformed by filter iterations. Then, the analysis allows both inference and proofs of the properties about the program variables that are tied to any such filter. 1
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Biological systems involve a wide amount of different molecular interactions. Each interaction can in turn present a deep level of mechanistic details. Most modelling methods can encompass only one of those two dimensions, that is the... more
Biological systems involve a wide amount of different molecular interactions. Each interaction can in turn present a deep level of mechanistic details. Most modelling methods can encompass only one of those two dimensions, that is the width or depth of biological systems. Rule-based modelling is a powerful method in that regard as it can model large systems with mechanistically detailed interactions. The advantage of including mechanistic details is that they allow a clear tracking of causal chains of events between biomolecules. This translates into a precise pinpointing of upstream regulators and a better understanding of complex biological systems.
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We propose a framework in which we share ghost variables across a collection of abstract domains allowing precise proofs of complex properties. In abstract interpretation, it is often necessary to be able to express complex properties... more
We propose a framework in which we share ghost variables across a collection of abstract domains allowing precise proofs of complex properties. In abstract interpretation, it is often necessary to be able to express complex properties while doing a precise analysis. A way to achieve that is to combine a collection of domains, each handling some kind of properties, using a reduced product. Separating domains allows an easier and more modular implementation, and eases soundness and termination proofs. This way, we can add a domain for any kind of property that is interesting. The reduced product, or an approximation of it, is in charge of refining abstract states, making the analysis precise. In program verification, ghost variables can be used to ease proofs of properties by storing intermediate values that do not appear directly in the execution. We propose a reduced product of abstract domains that allows domains to use ghost variables to ease the representation of their internal s...
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The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a math- ematical model is an important... more
The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a math- ematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the com- binatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate t...
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ASTRÉE was the first static analyzer able to prove automatically the total absence of runtime errors of actual industrial programs of hundreds of thousand lines. What makes ASTRÉE such an innovative tool is its scalability, while... more
ASTRÉE was the first static analyzer able to prove automatically the total absence of runtime errors of actual industrial programs of hundreds of thousand lines. What makes ASTRÉE such an innovative tool is its scalability, while retaining the required precision, when it is used to analyze a specific class of programs: that of reactive control-command software. In this paper, we discuss the important choice of algorithms and data-structures we made to achieve this goal. However, what really made this task possible was the ability interpretation framework. We discuss the way the precision of the semantics was tuned in ASTRÉE in order to scale up, the differences with some more academic approaches and some of the dead-ends we explored. In particular, we show a development process which was not specific to the particular usage ASTRÉE was built for, hoping that it might prove helpful in building other scalable static analyzers. This work was supported by the INRIA project-team ABSTRACTI...
Abstract. Rule-based modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules... more
Abstract. Rule-based modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexes-i.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matter- is the key to obtaining compact descriptions of what otherwise could be nearly infinite dimensional dynamical systems. This also makes these descriptions easier to read, write and modify. In the course of modelling a particular signalling system it will often happen that more traits matter in a given interaction than previously thought, and one will need to strengthen the conditions under which that interaction may happen. This is a process that we call rule refinement and which we set out in this paper to study. Specifically we present a method to refine rule sets in a way that preserves the implied stochastic ...
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We present a new numerical abstract domain. This domain automatically detects and proves bounds on the values of program variables. For that purpose, it relates variable values to a clock counter. More precisely, it bounds these values... more
We present a new numerical abstract domain. This domain automatically detects and proves bounds on the values of program variables. For that purpose, it relates variable values to a clock counter. More precisely, it bounds these values with the i-th iterate of the function [X ↦ → α×X+β] applied on M, where i denotes the clock counter and the floating-point numbers α, β, and M are discovered by the analysis. Such properties are especially useful to analyze loops in which a variable is iteratively assigned with a barycentric mean of the values that were associated with the same variable at some previous iterations. Because of rounding errors, the computation of this barycenter may diverge when the loop is iterated forever. Our domain provides a bound that depends on the execution time of the program.
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Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each others, which leads to the formation of a huge number of distinct chemical species (i.e. non-isomorphic... more
Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each others, which leads to the formation of a huge number of distinct chemical species (i.e. non-isomorphic connected components of proteins). Thus we cannot generate explicitly the quantitative semantics of these models, and even less compute their properties. Model reduction aims at reducing this complexity by providing another grain of observation. In this paper, we propose two unifying frameworks for combining model reductions: we propose a symmetric product operator for combining model reductions for stochastic semantics and we show how to abstract further existing reduced differential systems by the means of linear projections. We apply both frameworks so as to abstract further existing reduced quantitative semantics of the models that are written in Kappa, by taking into account symmetries among binding sites in proteins. Keywords: rules-based modeling,...
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In this paper, we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein-protein interaction networks. Our approach consists in quotienting the state space of networks. Yet... more
In this paper, we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein-protein interaction networks. Our approach consists in quotienting the state space of networks. Yet interestingly, we do not apply the widely-used strong lumpability criterion which imposes that two equivalent states behave similarly with respect to the quotient, but a weak version of it. More precisely, our framework detects and proves some invariants about the dynamics of the system: indeed the quotient of the state space is such that the probability of being in a given state knowing that this state is in a given equivalence class, is an invariant of the semantics. Then we introduce an individual-based stochastic semantics (where each agent is identified by a unique identifier) for the programs of a rule-based language (namely Kappa) and we use our abstraction framework for deriving a sound population-based semantics and a sound fragments-based sema...
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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or... more
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Intrinsic Information carriers in combinatorial dynamical systems Russ Harmer, Vincent Danos, Jérôme Feret, Jean Krivine, Walter Fontana
Sicherheitskritische eingebettete Systeme mussen hohen Qualitatsanforderungen genugen. Laufzeitfehler, z.B. arithmetische Uberlaufe oder Rundungsfehler konnen zu fehlerhaftem Programmverhalten fuhren. Da in der Regel keine vollstandige... more
Sicherheitskritische eingebettete Systeme mussen hohen Qualitatsanforderungen genugen. Laufzeitfehler, z.B. arithmetische Uberlaufe oder Rundungsfehler konnen zu fehlerhaftem Programmverhalten fuhren. Da in der Regel keine vollstandige Testabdeckung moglich ist, bieten sich statische Analysatoren an. Diese bieten eine vollstandige Coverage, konnen jedoch Fehlalarme erzeugen. Da jeder potentielle Laufzeitfehler manuell vom Benutzer uberpruft werden muss, kann eine hohe Zahl von Fehlalarmen dazu fuhren, dass echte Fehler ubersehen werden. Der statische Analysator Astree kann durch Spezialisierung und Parametrisierung an die zu analysierende Software angepasst werden. Dies ermoglicht kurze Analysezeiten und eine niedrige Zahl von Fehlalarmen. Astree wird z.B. bei der Zertifizierung von industrieller Flugzeugsteuerungssoftware eingesetzt. Safety-critical embedded software has to satisfy stringent quality.
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This paper reports the results of an ESA funded project on the use of abstract interpretation to validate critical real-time embedded space software. Abstract interpretation is industrially used since several years, especially for the... more
This paper reports the results of an ESA funded project on the use of abstract interpretation to validate critical real-time embedded space software. Abstract interpretation is industrially used since several years, especially for the validation of the Ariane 5 launcher. However, the limitations of the tools used so far prevented a wider deployment. Astrium Space Transportation, CEA, and ENS have analyzed the performances of two recent tools on a case study extracted from the safety software of the ATV: * ASTREE, developed by ENS and CNRS, to check for run-time errors, * FLUCTUAT, developed by CEA, to analyse the accuracy of numerical computations. The conclusion of the study is that the performance of this new generation of tools has dramatically increased (no false alarms and fine analysis of numerical precision).
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In this paper, we show how thread partitioning helps in proving properties of mobile systems. Thread partitioning consists in gathering the threads of a mobile system into several classes. The partitioning criterion is left as a parameter... more
In this paper, we show how thread partitioning helps in proving properties of mobile systems. Thread partitioning consists in gathering the threads of a mobile system into several classes. The partitioning criterion is left as a parameter of both the mobility model and the properties we are interested in. Then, we design a polynomial time abstract interpretation-based static analysis that counts the number of threads inside each partition class.
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Preuve Soit (E,+, •) un K-espace vectoriel. Soit I un ensemble fini. Une famille (ui)i∈I ∈ E d’éléments de E. — (⇒) Si (ui)i∈I est libre. I est un sous-ensemble fini de I. Puis par la définition 1.1, pour tout toute famille de scalaires... more
Preuve Soit (E,+, •) un K-espace vectoriel. Soit I un ensemble fini. Une famille (ui)i∈I ∈ E d’éléments de E. — (⇒) Si (ui)i∈I est libre. I est un sous-ensemble fini de I. Puis par la définition 1.1, pour tout toute famille de scalaires (λi)i∈I , on a : ∑ i∈I λi •ui = 0E ⇔ ∀i ∈ I, λj = 0. — (⇐) On suppose que pour tout toute famille de scalaires (λi)i∈I , on a : ∑ i∈I λi • ui = 0E ⇔ ∀i ∈ I, λj = 0. Soit J un sous ensemble fini de I. Soit (λj)j∈J ∈ K une famille de scalaire. On pose pour i ∈ I \ J , λi = 0. On a : ∀j ∈ J, λj = 0⇔ ∀i ∈ I, λi = 0, puisque pour tout i ∈ I \ J , λi = 0. Et, par hypothèse,
Site-graph rewriting languages as Kappa or BNGL supply a convenient way to describe models of signalling pathways. Unlike classical reaction networks, they emphasise on the biochemical structure of proteins. We use patterns to formalise... more
Site-graph rewriting languages as Kappa or BNGL supply a convenient way to describe models of signalling pathways. Unlike classical reaction networks, they emphasise on the biochemical structure of proteins. We use patterns to formalise properties about bio-molecular species. Intentionally, a pattern is a part of a species, but extensionally it denotes the multi-set of the species containing this pattern (with the multiplicity). Thus reasoning on patterns allows to handle symbolically arbitrarily big (if not infinite) multi-sets of species. This is a key point to design fast simulation algorithms or model reduction schemes. In this paper, we introduce the notion of extended patterns. Each extended pattern is made of a classical pattern and of a set of potential bonds between pairs of sites. Extended patterns have positive (when at least one of the potential bonds is realised) and negative (when none is realised) instances. They are important to express the consumption and the produc...
Site-graph rewriting languages as Kappa or BNGL supply a convenient way to describe models of signalling pathways. Unlike classical reaction networks, they emphasise on the biochemical structure of proteins. We use patterns to formalise... more
Site-graph rewriting languages as Kappa or BNGL supply a convenient way to describe models of signalling pathways. Unlike classical reaction networks, they emphasise on the biochemical structure of proteins. We use patterns to formalise properties about bio-molecular species. Intentionally, a pattern is a part of a species, but extensionally it denotes the multi-set of the species containing this pattern (with the multiplicity). Thus reasoning on patterns allows to handle symbolically arbitrarily big (if not infinite) multi-sets of species. This is a key point to design fast simulation algorithms or model reduction schemes. In this paper, we introduce the notion of extended patterns. Each extended pattern is made of a classical pattern and of a set of potential bonds between pairs of sites. Extended patterns have positive (when at least one of the potential bonds is realised) and negative (when none is realised) instances. They are important to express the consumption and the produc...
Un systeme mobile est un ensemble de composants qui peuvent interagir entre eux, tout en modifiant dynamiquement le systeme lui-meme. Ces interactions controlent ainsi la creation et la destruction des liaisons entre les composants, mais... more
Un systeme mobile est un ensemble de composants qui peuvent interagir entre eux, tout en modifiant dynamiquement le systeme lui-meme. Ces interactions controlent ainsi la creation et la destruction des liaisons entre les composants, mais aussi la creation dynamique de nouveaux composants au sein du systeme. La taille d'un tel systeme varie au cours du temps, elle n'est pas bornee en general. Un systeme mobile peut representer des reseaux de telecommunication, des systemes reconfigurables, des applications client-serveur sur la toile, des protocoles cryptographiques, ou des systemes biologiques. Plusieurs modeles sont disponibles selon le domaine d'application et la granularite du niveau d'observation. Dans cette these, nous proposons un cadre de travail unifiant pour decouvrir et prouver statiquement (avant leur execution) et automatiquement les proprietes des systemes mobiles. Nous proposons un meta-langage dans lequel nous encodons les modeles les plus couramment u...