Project Proposal

Theoretical Adverse Computations, and Safety

ThEorie des Calculs AdveRses, et securite

CARTE

Scientific leader:Jean-Yves MarionINRIA scientific and technological challenges: 1 3 and 1Keywords: Algorithmic, Complexity, Computability, Complex Systems, Algo-

rithms, Virus, Malwares, Networks, Computational Models, Resource Analysis,Program Properties, Termination, Formal Systems, Logic

1The seven INRIA scientific and technological challenges are:

1. Designing and mastering the future network and communication services infrastructures

2. Developing multimedia data and information processing

3. Guaranteeing the reliability and security of software-prevalent systems

4. Coupling models and data to simulate and control complex systems

5. Combining simulation, visualization and interaction

6. Modeling living beings

7. Fully integrating ICST into medical technology

1 Project-team composition

1.1 Permanent positions

• Full-time researchers

– Olivier Bournez, Charge de recherche INRIA.

– Johanne Cohen, Chargee de recherche, CNRS,

– Isabelle Gnaedig, Chargee de Recherche INRIA.

• Professors and assistant professors

– Guillaume Bonfante, Maitre de conferences, Ecole des Mines de Nancy,INPL

– Jean-Yves Marion, Professeur, Ecole des Mines de Nancy, INPL

1.2 PhD and Post-Docs

• Emmanuel Hainry, ATER, UHP

• Romain Pechoux, PhD MENRT,

• Matthieu Kaczmarek, BDI CNRS-Region,

• Marco Gaboardi, joint PhD with Turin University

• Octave Boussaton, PhD Henri Poincare University

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2 Main objectives

Algorithmic and programming theory define implicitly the semantics of an algo-rithm or a program. Thus, when an algorithm asks for a value, the request hasa meaning, like the weight of an arc, but this meaning is external to the algo-rithm. This characteristic is not shared by other sciences, whose semantic is notdefined, in general, in an external way by the scientist. Since the computationenvironment is made of autonomous systems, that have their own objectives,and since we try to take into account real world constraints, an algorithm cannotbe based on “a priori” knowledge from its environment. A network routing com-putation has to consider the economic importance of each independent agent.An antivirus has to determine the intentions of a program (potentially hostile)to do its task correctly. A program is asked to perform well, even if good clas-sical properties are not ensured. One of the main objectives of the CARTEproject is to take into account adversity, as a veritable full-fledged component,linked to actors of a computation, whose behavior is unknown or unclear. Wecall this notion adversary computation.

One of the main objectives is then to predict the behavior of adversarycomputations, to construct robust, i.e. fault-tolerant algorithms and systems,taking into account divergent interests, resisting viral attacks, and performingwell, even if certain correctness properties are missing. One of the original as-pects of the project is to combine the two following approaches. The first oneis the analysis of the behavior of a wide-scale system, using tools coming fromboth the Continuous and the Game Theories. Simply put, this is a macroscopicapproach. In the second approach, the tools we envisage using to build defenseswould come rather from logic, rewriting, and, more generally, from the Pro-gramming Theory. We will complete these two approaches with the control ofcomputations in antagonistic environments, which requires studying and ver-ifying the fundamental properties of programs and systems, like termination,stability or access to resources.

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3 Scientific foundations

We present the fundamental notions, formalisms and computational models wewill use for our purpose. This brief presentation is not exhaustive, but looks atthe areas in a particular way, enhancing the aspects which seem to us interestingto reach the goals we have fixed in our research directions.

3.1 Continuous Computation Theory

Today’s classical computability and complexity theory deals with discrete timeand space models of computation. But discrete time models of machines work-ing on a continuous space can be considered: consider for example the BlumShub and Smale machines of [6]. Recursive analysis, introduced by Turing [81],Grzegorczyk [50], and Lacombe [56] can also be considered as continous spacediscrete time computation theory.

Models of machines working with a continuous time and space can also beconsidered: see for example the General Purpose Analog Computer of ClaudeShannon [76], defined as a model of the Differential Analysers [20].

At its beginning, continuous time computation theory was mainly concernedwith analog machines. Determining which systems can actually be consideredas computational models is a very intriguing question. This relates to the philo-sophical discussion about what is a programmable machine, which is beyondthe scope of this discussion. Nonetheless, there are some early examples of builtanalog devices that are generally accepted as programmable machines. Theyinclude Bush’s landmark 1931 Differential Analyzer [20], as well as Bill Phillips’Finance Phalograph, Hermann’s 1814 Planimeter, Pascal’s 1642 Pascaline, oreven the 87 b.c. Antikythera mechanism: see [25]. Continuous time computa-tional models also include neural networks and systems that can be built usingelectronic analog devices. Since continuous time systems are conducive to mod-eling huge populations, one might speculate that they will have a prominentrole in analyzing massively parallel systems such as the Internet [72].

The first true model of a universal continuous time machine was proposed byShannon [76], who introduced it as a model of the Differential Analyzer. Dur-ing the 1950s and 60s an extensive body of literature was published about theprogramming of such machines2. There were also a number of significant pub-lications on how to use analog devices to solve discrete or continuous problems:see e.g. [82] and the references therein. However, most of this early literature isnow only marginally relevant given the ways in which our current understandingof computability and complexity theory have developed.

The research on artificial neural networks, despite the fact that it mainlyfocused on discrete time analog models, has motivated a change of perspectivedue to its many shared concepts and goals with today’s standard computabilityand complexity theory [70], [69]. Another line of development of continuoustime computation theory has been motivated by hybrid systems, particularly

2See for example the very instructive Doug Coward ’s web Analog Computer Museum [25]and its bibliography.

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by questions related to the hardness of their verification and control: see forexample [18] and [4].

In recent years there has also been a surge of interest in alternatives toclassical digital models other than continuous time systems. Those alternativesinclude discrete-time analog-space models like artificial neural networks [70],optical models [87], signal machines [29] and the Blum Shub and Smale model[7]. More generally there have also been many recent developments in non-classical and more-or-less realistic or futuristic models such as exotic cellularautomata models [48], molecular or natural computations [51], [2], [57], [73],black hole computations [53], or quantum computations [28], [49], [77], [54].

The computational power of discrete time models are fairly well known andunderstood thanks in large part to the Church-Turing thesis. The Church-Turing thesis states that all reasonable and sufficiently powerful models areequivalent. For continuous time computation, the situation is far from beingso clear, and there has not been a significant effort toward unifying concepts.Nonetheless, some recent results establish the equivalence between apparentlydistinct models [47], [46], [45], and [16], which give us hope that a unified theoryof continuous time computation may not be too far in the future.

A survey on continuous-time computation theory co-authored with ManuelCampagnolo can be found in [15]. This survey includes open problems and re-search directions. Extended discussions can also be found in [14]. This presenta-tion is extracted from [15]. A monograph on complexity theory for discrete-timecomputation over the real and over arbitrary structures in the sense of [6] canbe found in [7] and [74] respectively.

3.2 Rewriting

The rewriting paradigm, initially developed to mechanize the word problem, i.e.to decide whether an equality between terms is true modulo a set of axioms, hasbeen greatly studied, in the context of automated deduction, especially sincethe seventies. Rewriting a term, with a set of rules that are oriented axioms,consists in deciding through matching whether a part of the term to be rewrittenis an instance of a left-hand side of rule, then in replacing this instance in theterm by the corresponding instance of the right-hand side.

Properties of this deduction mechanism like confluence, sufficient complete-ness, consistency, or various notions of termination, have been described. Forthese generally undecidable properties, many proof methods have been devel-oped for basic rewriting and in a weaker proportion, for extensions like equa-tional extensions, consisting of rewriting modulo a set of axioms, conditionalextensions where rules are applied under certain conditions only or typed orconstrained extensions. Completeness test algorithms, a great number of meth-ods to prove termination, most founded on orderings or on decreasingness argu-ments, and completion procedures to ensure confluence are now at our disposi-tion [23, 26, 5, 27, 79].

Rewriting has reached some maturity and the rewriting paradigm is nowwidely used. It allows for easily expressing deduction systems in a declarative

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way, for expressing complex relations on infinite sets of states in a finite way,provided they are countable. It also provides a semantics for programming lan-guages and environments. Let us cite ASF+SDF [17], Maude [21], CafeOBJ [42],ELAN [13], Stratego [83], or Tom [65], now currently used for any kind of appli-cation.

An interesting aspect of this paradigm is that it allows automatable or semi-automatable correctness proofs on the systems or programs. Indeed, propertiesof rewriting systems as those cited above are translatable to the deduction sys-tems or programs they formalize, and the proof techniques may directly applyto them.

Another interesting aspect of rewriting is that it allows characteristics orproperties of the modelized systems to be expressed as equational theorems,often automatically provable using the rewriting mechanism itself or induction-less induction techniques based on completion [75]. Note also that the rewritingand the completion mechanisms also allows transformation and simplificationof formal systems or programs.

Nevertheless, an important stake in the domain is now to adapt and com-plete the previous techniques to the real needs of modelizing and programming.The proof techniques for the above cited rewriting properties or the equationaltheorems still need to be refine to take into account the extensions of rewritingallowing to give a realistic description power. The need is especially importantin the adversary case, for example when key properties like termination are notensured.

3.3 Algorithmic game theory

Game theory aims at discussing situations of competition between rational play-ers [71]. After the seminal works of Emile Borel and John von Neumann, onekey events was the publication of the book [85] published in 1944 by John vonNeumann and Oskar Morgenstern. Game theory then spent a long period inthe doldrums. Much effort was devoted at that time towards the mathematicsof two-persons, zero-sum games.

For general games, the key concept of Nash equilibrium was proposed in theearly 50s by John Nash in [67], but it was not until the early 70s that it was fullyrealized what a powerful tool Nash has provided in formulating this concept.This is now a central concept in economics, biology, sociology and psychologyto discuss general situations of competition, as attested for example by severalNobel prizes of Economics.

Even if the theory of repeated games allows to model some dynamical as-pects, one can say that this stays a theory to discuss static situations of equilibriabetween rational players [71].

Evolutionary game theory originated as an application of the mathemat-ical theory of games to biological contexts, arising from the realization thatfrequency dependent fitness introduces a strategic aspect to evolution. Thistheory introduced by [62] can be considered as the application of populationdynamicalal methods to game theory [52, 86].

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Algorithmic game theory differs from game theory by taking into accountalgorithmic and complexity aspects, as historically main developpments of clas-sical game theory have been realized in a mathematical context, without trueconsiderations on effectivness of constructions.

Game theory and algorithmic game theory have large domains of applica-tions, even in theoretical computer science: it has been used to understand com-plexity of problems linked to equilibrium [63], the loss of performance due toindividual behavior in distributed algorithmics [72, 3, 24], the design of provoca-tive mechanisms [68], the problems related to the pricing of services in someprotocols [30], auction problems, etc [19] . . .

3.4 Computer virology

The literature which explains and discusses about practical issues is quite ex-tensive, see for example Ludwig’s book [58] or Szor’s one [78]. But, we thinkthat the best reference are both books of Filiol [31] (English translation [32])and [34]. However, there are only a few theoretical/scientific studies, which at-tempt to give a model of computer viruses. This situation is improving withthe new journal of computer virology and the workshop TCV that we are or-ganizing. (Indeed, other conferences are either purely technical, like SSTIC inFrance, or organized by anti-virus companies.)

From an historical point of view, the first official virus appeared in 1983 onVax-PDP 11. In the very same time, a series of papers was published whichalways remain a reference in computer virology: Thompson [80], Cohen [22]and Adleman [1]. In a seminal work, Cohen defines viruses with respect toTuring Machines. For this, he considers viral sets. A viral set is a pair (M,V )constituted of a Turing Machine M and a set of viruses V . When one runs onM a virus v of V , it duplicates or mutates to another virus of V on M ’s tape.Adleman [1] takes a more abstract formulation of computer viruses based oncomputability theory in order to have a definition independent from a partic-ular computational model. The most important contributions of Adleman iscertainly to develop scenarios, which describe, and classify how a virus behaveswith respect to some environment. From this study, and from the current pointof views like the ones that we find in Filiol’s book[31] or Szor’s one [78], a virusis characterized by

1. A virus infect programs by modifying them

2. A virus copies itself and can mutate

3. Virus spreads throughout a system

So, a virus is essentially a self-replicating program inside an adversary envi-ronment. More precisely we establish in [10] that Kleene’s second recursiontheorem [55] is the cornerstone from which viruses and infection scenarios canbe defined and classified. It is essential to understand that computer virologyhas a strong theoretical foundation, which is based on self-replicable systems

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and evolving fixed points, that is a fixed point which modifies its code eachtime. Thus, by replacing “automaton” by “virus”, the following citation of vonNeumann is inspiring [84]: ”Can an automaton be constructed, i.e., assembledand built from appropriately ”raw material”, by another automaton? . . .Can theconstruction of automata by automata progress from Simpler types to increas-ingly complicated types?”.

The above scientific foundation justifies our position to use the word virusas a generic word for self-replicating malwares. (There are yet a difference. Amalware has a payload, and virus may not have one.) For example, worms arean autonous self-replicating malwares and so fall into our definition. In fact, thecurrent malware taxonomy (virus, worms, trojans, . . . ) is unclear and subjectto debate.

The crucial question is how to detect viruses or self-replicating malwares.Cohen demonstrated that this question is undecidable. The anti-virus heuris-tics are based on two methods. The first one consists in searching for virussignatures. A signature is a regular expression, which identifies a family ofviruses. There are obvious defect. For example, an unknown virus will not bedetected, like ones related to a 0-day exploit. We strongly suggest to have a lookat the independent audit [33] in order to understand the limits of this method.The second one consists in analysing the behaviour of a program by monitoringit. Following [35], this kind of methods is not yet really implemented. Moreover,the large number of false-positive implies this is barely usable. To end this shortsurvey, intrusion detection encompasses virus detection. However, unlike com-puter virology, which has a solid scientific foundation as we have seen, the IDSnotion of “malwares” with respect to some security policy is not well defined.The interesting reader may consult [66].

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4 Research directions

The scientific project is divided into three parts. The first part focuses on com-putation models and in particular on continuous system and rewriting systems.This part is the scientific foundations on which the two other parts are based.The two other parts consider adversity, as a full-fledged component, linked toactors of a computation, whose behavior is unknown or indistinct. The objectiveof the second part is to study robust and distributed algorithms. Our approachwill use algorithmic game theory and so will use continuous dynamic systems.The last part concerns computer virology. This part needs both first parts. In-deed, our approach tries to use formal methods in order to prevent viruses, andalso to develop algorithms over large distributed systems in order to understandthe evolution of a virus attack with respect to agent policies.

4.1 Computations by Dynamical Systems

Participants : Olivier Bournez, Guillaume Bonfante, Isabelle Gnaedig, Jean-Yves Marion

The dynamical system model is a very general mathematical model.In general, a dynamical system can be defined as the action of a subgroup

T of R on a space X, i.e. by a function (a flow) φ : T ×X → X satisfying thefollowing two equations

φ(0, x) = x (1)

φ(t, φ(s, x)) = φ(t + s, x). (2)

It is well known that subgroups T of R are either dense in R or isomorphicto the integers. In the first case, the time is termed continuous, in the lattercase, discrete. A dynamical system whose space is discrete and that evolvesdiscretely is termed digital, otherwise it is analog

Since flows obtained by solutions of ordinary differential equations satisfyequations (1) and (2), they correspond to specific continuous time and spacedynamical systems. Although not all continuous time and space dynamicalsystems can be put in a form of a differential equation, ordinary differentialequations are sufficiently general to cover a very wide class of such systems.In particular, if φ is continuously differentiable, then y′ = f(y), with f(y) =ddtφ(t, y)

∣∣t=0

, describes the dynamical system. For discrete time systems, wecan assume without loss of generality that T is the integers. The analog of thisdifferential equation dy

dt = f(y) is a recurrence equation y(t + 1) = f(y(t))Most of the continuous time models described above have a continuous dy-

namics described by differential equations, hence by continuous time and spacedynamical systems. Rewriting theory can be considered as a tool for describ-ing discrete space and time dynamical systems over the set of terms of a givensignature. Models from evolutionary game theory are also particular dynamicalsystems models.

It follows that understanding computational properties of these systems, aswell as the hardness of the analysis and the verification of properties for these

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systems turns out to be very closely related problems that can be formulateduniformly as understanding algorithmic complexity of decision problems for dy-namical systems.

For example, as an undecidability proof is often obtained by simulating aTuring machine, an undecidability proof for verification of a given property oftenyields that the considerd class of dynamical systems has at least the powerof universal Turing machines. Conversely, most of the results motivated bycomputation theory for dynamical systems yields direct lower bounds on thehardness of their verification.

Dynamical systems in our sense are formal entities allowing to modelize orcompute, evoluting during the time in an explicit or implicit way. We wouldlike to study in particular models for dynamical systems having a continuousbehavior, and properties of dynamical systems having an adversary behavior.

Continuous systems computation theory Some systems carrying out com-putations are intrinsically continuous. This is the case, for example, of somemore or less futuristic models such as quantum models of computations, ormodels based on space-time curves, but also of some quite real mechanical orelectronic machines. In particular, the progress of analog electronics allows forthe possibility of reintroducing purely analog machines. By the way, the under-lying models of all the components of today’s computers are analog, even if fortechnological reasons, and also for historical choices, digital electronics imposeditself to the detriment of analog electronics.

Furthermore, even for intrinsically discrete models, as soon as the numberof individuals is high, natural models become continuous. To characterize, forexample, a population of processors in a given state at a given time, it is morenatural to talk about proportions of individuals with a given property thantalking directly about the individuals (i.e. of statistics or probabilities). Onecan then talk about the dynamicals of these populations in a natural way.

Observe that this constitutes an abstraction of huge-sized systems, which isquite unusual in classical complexity/computability/algorithmic, but natural,and abundantly used in many of other sciences, like biology or physics.

Our long term objectives are to try to answer the following questions:

1. How can we model, in a robust and satisfactory way, continuous systemsor systems close to continuous systems?

2. How can we characterize the computing power, at the level of complexityand calculability of the systems obtained?

3. Is there a robust theory of computability for continuous machines?

4. Is there a robust theory of complexity for continuous machines?

5. How can we use the power of continuous machines for the resolution ofdigital problems?

For the middle term, our objectives are the following:

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• compare the classes of algebraic models resulting from R-recursing func-tions [64], and the model of GPAC of Shannon [76], with recursive analysis,

• present results about the complexity of solving differential equations, thatallow for extracting upper bounds on the power of some models,

• use continuous time computation theory to discuss the computationalproperties of macroscopic population models.

Analysis and verification of adversary systems The other research di-rection we are interested in on dynamical systems is the study of propertiesof systems or programs in the context of adversary computations. We wouldlike to offer proof and verification tools for properties of systems and programs,whose behavior is unknown or indistinct, to guarantee the correct behavior ofthese systems or programs.

We have been working for several years on the analysis of systems and theproperties of programs, and we have the intention to carry on with our effortsin this direction, to complete the previous objectives.

We are interested in continuous and hybrid systems. In a mathematicalsense, a hybrid system can be seen as a dynamical system, whose transitionfunction does not satisfy the classical regularity hypotheses, like continuity, orcontinuity of its derivative. The properties to be verified are often expressedas reachability properties. For example, a safety property is often equivalentto (non-)reachability of a subset of unsure states from an initial configuration,or to stability (with its numerous variants like asymptotic stability, local sta-bility, mortality, etc . . . ). Thus we will essentially focus on verification of theseproperties in various classes of dynamical systems.

We are also interested in the analysis methods of rewriting properties. Formore than five years, we have been developing specific procedures for propertyproofs of rewriting, for the sake of programming, in particular with inductivetechniques, already applied with success to termination under strategies [42, 43,44, 46], to sufficient completeness [50], and to probabilistic termination [44].

The three last results take place in the context of adversary computations,since they allow for proving that even a divergent program, in the sense whereit does not terminate, can give the expected results.

We also study the links between the different properties of programs tocoordinate and optimize the use of the tools allowing to prove them.

We will continue this study, as well as the development of our inductiveapproach, which seems to be general enough to be extended to different aspectsof adversary computations.

We especially intend to continue to study the termination property, andits impact on other properties, since it seems to be central in several researchdirections retained by the project:

• until now it was very used for deciding properties like confluence, com-pleteness or consistency. Its weakening or its absence, very frequent inreal cases, throws us into the context of adversity,

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• it is a tool for the analysis of resources,

• thoroughly analyze divergence by non-termination phenomenon can be anapproach for modeling the continuous.

A crucial element of safety and security of software systems is the prob-lem of resources. We are working in the field of Implicit Computational Com-plexity. Interpretation based methods like Quasi-interpretations (QI) or sup-interpretations, are the approach we have been developing these last five years,see [6, 52, 9, 24, 20] and the ACI project CRISS.

• Interpretation based methods, like QI, provide static analysis of the com-plexity of programs. These approaches apply to functional, reactive orobject programming languages.

• There are quite efficient heuristics to find the QI or SI of programs. Weare currently developing the CROCUS system (following the former ex-perimental software ICAR) to synthesize QIs.

Our middle-dated terms are the following:

• to carry on with our study of property proof coordination, and extendour inductive approach to other properties like confluence, and to otherdeduction mechanisms besides rewriting, in the context of adversary com-putations,

• to carry on on some theoretical aspects of implicit computational com-plexity, more precisely on ramified recursion and light logics.

• to carry on with our efforts on quasi-interpretations. In particular, we willmake every effort to built a system that will be able to automatically inferthe resources of a program.

• to analyze the work linking the termination proof of rule-based systems tothe complexity of derivation chains, for a modelization of the continuous.

4.2 Robust and distributed algorithms, algorithmic gametheory

Participants : Olivier Bournez, Johanne Cohen, Jean-Yves MarionOne of the problems related to distributed algorithmics corresponds to the

minimization of resources (time of transit, quality of services) in problems oftransiting information (routing problems, group telecommunications) in telecom-munication networks.

Each type of network gives rise to natural constraints on models. For ex-ample, a network is generally modeled by a graph. The material and physicalconstraints on each component of the network (routers, communication media,topology, etc . . . ) result in different models. One natural objective is then tobuild algorithms to solve these types of problems on various types of models.

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One can also impose proposed solutions to offer certain guarantees: for examplethe property of self-stabilization, which expresses that the system must end in acorrect state whatever its initial state; or certain guarantees of robustness: evenin the presence of a small proportion of Byzantine actors, the final result willremain correct; even in the presence of rational actors with divergent interests,the final result will remain acceptable.

Algorithms of traditional distributed algorithmics were designed with thestrong assumption that the interest of each actor does not differ from the interestof the group. For example, in a routing problem, classical distributed algorithmsdo not take into account the economic interests of the various autonomous sys-tems, and only try to minimize criteria such as shortest distances, completelyignoring the economical consequences of decisions for involved agents.

If one wants to have more realistic models, and take into account the waythe different agents behave, one gets more complex models.

However, today, one gets models on which this is rather hard to reason. Forexample,

• models of dynamism are missing: e.g., how to model a negotiation ina distributed auction mechanism for the access to a telecommunicationsservice,

• only few methods are known to guarantee that the equilibrium reached bysuch systems remains in some domains that could be qualified as safe orreasonable,

• there is almost no method discussing the speed of convergence, when thereis convergence,

• only a little is known about the time and space resources necessary toestablish some techniques to guarantee correct behavior.

Thus, it is important to reconsider the algorithms of the theory of distributedalgorithmics, under the angle of the competitive interests that involved agentscan have (Adversary computation). This requires to include/understand wellhow to reason on these types of models. The long-term objectives are thefollowing:

• characterize the associated mechanism theory. The objective is to in-clude/understand which properties can be guaranteed, for a given conceptof equilibrium,

• understand the limits of these theories,

• reconsider the problems of optimization of resources in telecommunicationsnetworks, taking into account the fact that each involved agent can havea divergent interest from that of the group.

At middle-term, our objectives are the following:

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• Present a model of protocol, such as inter-domain routing, utilizing eco-nomic aspects, with proved guarantees.

• Produce relevant concepts of equilibrium for these models, and relevantconcepts for their dynamics.

• Produce classes of strategies that lead in a proven way to these notions ofequilibrium, and discuss associated proof techniques.

4.3 Computer Virology

Participants : Guillaume Bonfante, Isabelle Gnaedig, Jean-Yves MarionFrom an epistemological point of view, it is rightful to wonder why there

is only a few fundamental studies on computer viruses while it is one of theimportant flaws in software engineering. The lack of theoretical studies explainsmaybe the weakness in the anticipation of computer diseases and the difficultyto improve defenses. For these reasons, we do think that it is worth to explorefundamental aspects.

Following the introductory part, a virus is a program which is the solutionof fixed point equations. Solutions are provided by variant of Kleene’s recursionTheorem. In [8], we have tired to show how to build ”highly”metamorphic viruscompilers. We think that this line of research should be pursued in order (i)to define what is a computer in different programming languages and setting,(ii) to take into consideration resources like time and space. The next objectiveshould be to define security policies and the mechanisms that implement them inorder to prevent attacks. This goal require good understanding of point (i) and(ii) above. We think that formal methods like rewriting, type theory, logic, orformal languages, should help to define the notion of a formal immune system,which defines a certified protection, that we try to developp. Lastly, we haveconstructed tools to analyze system resources [11], which might be useful toavoid attacks by memory overflow to take control of a system.

Then, we are working on virus detection. We have already explained thecurrent methods. We are developing a detection algorithms based on an ab-straction of the control flow graph of programs. The idea is to compare controlflow graphs of malware with the one of a target program. The experimentsthat we have made are quite successful. From a theoretical point of view, thisapproach leads us to work with tree regular languages whose symbols as non-constant arity. In the last direction, we try to change the scale of our pointof view. Viruses spread through networks which might be seen as a very largedistributed system. Virus epidemic could be then represented as a game whereagents have different interest. So, the question is can we define reasonable politi-cies in such setting which integrate the interest of each partner. Related to this,we could also look biological immunology.

The long-term objectives are the following:

• Define security policies and mechanisms against malware by analyzingdata-flow by means of type systems.

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• Consider defenses based on an analogy with biological immune systems.

At middle-term, our objectives are the following:

• To study the foundation of computer virology

• To design a detection methods based on tree regular languages by flowgraph matching.

This study on computer virology leads us to propose and construct a “highsecurity lab” in which experiments can be done in respect with the French law.This project of “high security lab” in one of the main project of the CPER2007-2013.

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5 Applications

Our project aims at building the necessary theoretic approach to the settingof applications linked to computer science security. We have chosen to presentapplications either lying on current contractual research, or carrying on finishedcontractual research.

• The ARA SOGEA and the CPER SSS operation TATA. The ARA SO-GEA aims to contribute to the algorithmic game theory, in studying theproblems linked to adversary, to the game dynamic and to the complexityproblems linked to games. The SSS operation TATA is a starting collab-oration with economists on algorithmic game theory.

• The ARA VIRUS. The computer virology will focus our efforts in thecontext of the ARA SSIA Virus in collaboration with Eric Filiol (ESAT).Today, the definition of the defense policy against viral attacks is an appli-cation emerging from this recent research subject. The CPER SSS “Highsecurity laboratory” aims to build the condition with respect to the lawto make experiments on attacks and defences.

6 Software

CARIBOO

In the context of our study of rule-based program proof and validation, wedevelop and distribute CARIBOO (http://protheo.loria.fr/softwares/cariboo/),an environment dedicated to specific termination proofs under strategies likethe innermost, the outermost or local strategies.

Written in Elan and Java, it has a reflexive aspect, since Elan is itself arule-based language. CARIBOO was partially developed in the Toundra QSLproject, and reinforced in the framework of the Modulogic ACI [1, 2].

CROCUS

The CROCUS software aims at synthesizing quasi-interpretations. It takes pro-grams as input and returns the corresponding quasi-interpretation. Doing this,it can guarantee some bounds on the memory used along computations by theinput program. The currently analyzed programs are written in a subset of

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the CAML language, more precisely a first-order functional language subset ofCAML.

7 Expected results and success criterions

We are conscious of the ambition of the proposed project, all the more becausesome research subjects are new for us. Thus, several of us have changed disci-plines, which does not go without risk. But taking risk is stimulating and mo-tivates our activities. The usual success criterions apply to this project, whichcan be measured by the number of publications, applications development, orpatents. However, for the short-term, it seems to us that the first challenge isto move the gears of the described research subjects to mutually enrich them.

It is clear that the network inspired models have to do with software in-fections; in the same way, the rewriting inspired tools have applications in thestudy of the described computation models; also taking into account the contin-uous in computation models has to do with adversary computations. We haveemphasized four general objectives for our project:

• to propose a robust computation theory for continuous systems,

• to propose a methods against viruses,

• to understand limits of distributed algorithms with possibly antagonistinterests,

• to realize property proofs for a robust computation in antagonist environ-ments.

To reach them, we will rely on the research subjects contained in the project,which we master well, and on others, which we just address, like virology. Forthis last subject, a success criterion for us would be to combine the efforts ofthe research community on the topic.

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8 Collaborations

8.1 At INRIA

• Calligramme - INRIA Lorraine : As several people involved in thisproject come from this group, we still have some relations. The objectof Project Calligramme is the development of tools and methods stem-ming from proof theory, especially linear logic with a strong applicationin computational linguistics. We share methods but our research goalsand applications are different. In particular, we focus on complexity andadverse computations, which are not anymore a Calligramme subject.

• Protheo - INRIA Lorraine : As several people involved in this projectcome from this group, we still have some relations. The Protheo projectaims at designing and implementing tools for program specification andverification. We share methods but our research goals and applications aredifferent. Indeed, we focus on program analysis in the context of adversarycomputations, and also nex model of computations

• Grand-Large - FUTURS: several people of the Grand Large INRIAproject are involved in the SOGEA project that we are leading. ProjectGRAND LARGE works in the framework of large scale computing and theGlobalization of Computer Resources and Data (GRID) initiative. Ourpoint of view is more fundamental and we focus on complexity, on gametheory, and model of computations.

8.2 National Collaborations

• LITA- Metz University : We have regular research discussions withMaurice Margenstern’s team in this Lab. A part of the LITA lab focuseson properties of molecular models of computations (DNA models), ontiling problems, and on cellular automata.

• LIPN - Universite Paris 13 : Jean-Yves Marion and Guillaume Bon-fante have closed relations with P. Baillot, V. Mogbil, and P. de Nauroisabout control of resources. Their work involves the light fragment of linearlogic.

• Laboratoire de virologie et de cryptologie - Ecole Superieure etd’Application des Transmissions : We have started a collaborationwith Eric Filiol.

• Laboratoire PRiSM - Universite de Versailles, St-Quentin enYvelines, Equipe ALCAAP : We collaborate with several members ofthis lab, in particular since they are involved in the SOGEA project. Theirproblematic is about algorithmic for graphs and combinatorial analysis.

• LRI, Paris XI, Orsay We collaborate with several members of this lab,in particular since they are involved in the SOGEA project. We collaborate

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with people from the “Algorithms and Complexity” groups and with the“Parallelism” group.

• LIRMM, Montpellier We collaborate with several members of this lab,in particular with Rodolphe Giroudeau and Jean-Claude Konig. Our col-laborations are related to approximation algorithms for scheduling prob-lems.

• Paris VII: We are working with several people like R. Amadio on resourceanalysis and S. Grigorieff on various topics around computational modelsand complexity..

8.3 International Collaborations

• Computability in Europe Network. Several members of this projectare members of this network. Olivier Bournez is leading the French node ofthis project. It focuses on complexity and computability aspects, and hasrecently created a conference series, with conferences planed until 2010.

• APPSEM II Network. We collaborate with this network. Its objectiveis to promote research about semantic oriented applications of program-ming languages. Jean-Yves Marion is the LORIA leader of this network.

• ICC/LCC group. Jean-Yves Marion is member of the steering com-mitee of the group “Logic and Computational Complexity”. Jean-YvesMarion and Guillaume Bonfante collaborate with people in this group: D.Leivant (USA), J. Royer (USA), N. Jones (Denmark-DIKU), M. Hofmann(Germany-Munich), Niggl (Germany-Illmenau), Terui (Japan).

• City University, Hong Kong. Paulin de Naurois defended a PhD thesisco-supervised by Olivier Bournez, Jean-Yves Marion and Felipe Cucker inCity University.

• Portugal, Integrated Action Program Pessoa

– Olivier Bournez is leading a PAI with Instituto Superior Technicoin Lisbon. This program concerns the investigation on complexityand computability of continuous time models. Daniel Graca, PhDstudent there, spent more than one year with us in Nancy.

– Jean-Yves Marion is leading a PAI with Lisbon University. Thisprogram concerns characterizations of parallel complexity classes.

• Politecnico de Turin : We have collaboration with several people inTurin, in particular with Simona della Ronchi. Jean-Yves Marion co-supervises M. Gaboardi’s PhD thesis. Jean-Yves Marion is the LORIAleader of Franco-Italian project ”geometry of computations”.

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8.4 Industrial collaborations

We have regular contact with industrial partners. For instance, France Telecomand CRIL technologie are partners of the RNTL project.

Two PhDs have also been realized in collaboration with industrial partners.Florent Garnier’s PhD, co-directed by Olivier Bournez, was funded by FranceTelecom through the RNTL project. Liliana Ibanescu’s PhD, also co-directedby Olivier Bournez, was realized in partnership with PSA.

Concerning verification of hybrid systems (LIAFA and Verimag), and net-work algorithms, we have informal industrial collaborations.

8.5 Participation to national projects

• ACI Modulogic : Modulogic is an ACISI project, whose objective is tobuild an integrated toolbox for asserted software. This toolbox allows forwriting modules built on declaration, definitions, statements and proofs.Declarations can be refined into definitions and statements into proofs, byprogressively migrating from the specification to the implementation, withinheriting and redefining mechanisms, and by instantiating parameters.Isabelle Gnaedig is the head of the project for Nancy.

• ACI “securite” Criss : The objective of this project is to analyze pro-gram resources of reactive programs. The main theoretical notion forsuch analysis is based on quasi-interpretation. This project is related tothe former IST MRG (Mobile resource guarantees). Jean-Yves Marion isthe local head of this project and Guillaume Bonfante participates in it.

• ACI “nouvelles interfaces des mathematiques” Geocal : The ob-jective of Geocal is to study links between logics and the different fieldsof computer science. In particular, we focused on logics and complexity.Jean-Yves Marion is the local head of this project and Guillaume Bonfanteparticipates in it.

• Pole Rescom - GDR ASR : This national research group focuses onalgorithmics for telecommunications networks. We are involved in it, andJohanne Cohen has participated in its annual meetings over the last fewyears.

• Network“Complexite, Modeles Finis, Bases de Donnees”of GDRIM : Jean-Yves Marion, Guillaume Bonfante, Olivier Bournez and Em-manuel Hainry are members of this network. It mainly focuses on thecomplexity theory in a wide sense. Olivier Bournez and Emmanuel Hainryparticipate in their meetings and presented talks in 2004, 2005 and 2006 atthe annual meeting. Olivier Bournez and Emmanuel Hainry co-organizedwith Dider Galmiche the 2007 annual meeting. This network is a workinggroup of the GDR Informatique Mathematique.

• Group LAC of GDR IM We all participate in this GDR group.

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• Reseau RNTL“Averroes” : We participate in the RNTL project Aver-roes, whose objective is the analysis and verification for the reliability ofembedded systems, in particular concerning their quantitative and func-tional properties.

• ARA Sogea : Olivier Bournez is the national scientific coordinator of theARA Sogea (Security Of Games Equilibria and Distributed Algorithms).More details on this action can be found on http://sogea.loria.fr. JohanneCohen and Olivier Bournez are members of this ARA. Several other na-tional teams in Paris II, Paris XI, Versailles University are involved in thisproject.

• ARA Virus : Jean-Yves Marion is the head of the ARA Virus, whose goalis to establish a theory of computer viruses, and to built secure protectionsystems against them. Guillaume Bonfante also participates in the project.

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9 Positioning Within the Scientific Community

9.1 Models of Computations, Computability, Complexity

On a worldwide scale, many research teams focus on questions related to com-putability and complexity theory. For example, we are involved in the Com-putability in Europe (CiE) Network, which is a network of people interested inthe computability theory. In the French world, several research teams are ex-plicitly concerned by complexity theory, for example in LRI at Orsay, in Greycin Caen, in LIP in Lyon, in LITA in Metz, in LIPN in Paris XIII.

Compared to classical approaches, we mainly focus on non classical models ofcomputations, in particular on models of computations related to computationsover continuous domains, or inspired by huge parallelism models, or by viruses.

In that spirit, our closest competitor in France is the MC2 Team in Lyon,which focuses on models of computations. However, they mainly focus on cel-lular automata, or on quantum computations, or on Blum Shub and Smale, orValiant Model. Our models are distinct.

Concerning continuous time models, at the worldwide level, the models onwhich we focus are mainly studied by people involved in the CiE network. Inparticular, several people from Lisbon, with whom we collaborate closely, focuson continuous time models of computations. The new CIM research team fromENS Paris also focuses on properties of continuous dynamic systems, and ontheir properties, with a distinct point of view.

Concerning the models inspired by networks, the closest models that areconsidered in literature are mainly studied by people from Yale University inthe USA with the population protocol model. More classical models for hugesize parallelism include cellular automata. Several research teams worldwidefocus explicitly on cellular automata.

9.2 Robust and adversary algorithmics

Adverse Computations The term adverse computation is a terminology ofour own. One classical approach to model competition is the game theory. Thegame theory was invented by mathematicians, and is mainly used today byeconomists or biologists. As such, a huge number of research teams in thesefields have considerations related to the game theory.

The Algorithmic Game Theory differs from the game theory by the fact thatalgorithmic aspects are taken into account. The Algorithmic Game Theory,in full development for about 7 years, is mainly studied by people working oncomplexity aspects. Recent years have seen the emergence of its applications invarious research fields, including algorithmics for networks. Compared to themost common approach, we focus on dynamic aspects. Only a few papers havebeen devoted to this subject, in the computer science and algorithmic commu-nities. This is one of the research goals of the European DELIS project, and ofthe SOGEA project. The goal of DELIS is to develop methods, techniques andtools to cope with challenges imposed by the size and dynamics of today’s and

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especially future information systems, in an interdisciplinary effort of ComputerScience, Physics, Biology, and Economy. Compared to DELIS, we focus on al-gorithmic aspects, and on computation theoretic aspects with models comingfrom classical and continuous computation theory.

Another approach is given by computer virology whose positioning is ex-plained below.

Distributed Algorithms At a worldwide level, several research teams focuson problems related to algorithmics for networks. At the French level, we canmention research teams in LIRMM in Monptellier, LIP and INSA in Lyon, LRIin Orsay, PRiSM in Versailles, LIAFA in Paris VII, IBISC in Evry, LABRI inBordeaux. All of these teams are involved in the ResCom network, in which weparticipate.

Classical approaches are mainly based on properties of graphs, and proto-cols. The current project proposes to use theoretic game considerations in theconstruction of algorithms for networks. At the French level, people that alsoconsider similar arguments include some members of the IBISC lab in Evry,mainly focusing on scheduling problems, the LIA in Avignon, mainly focusingon problems related to pricing, in PRiSM, with whom we collaborate, and inIRISA in Rennes. Most of these people are involved in the EURONGI Europeanproject.

We are also involved in the French ARA SSIA SOGEA project with some ofthem. The SOGEA project focuses on dynamic aspects and complexity ques-tions, in relations with applications for telecommunication and sensor networks.At a worldwide level, the closest project is the European DELIS project, inwhich no French computer scientist is involved.

Analysis and Verification of Adversary Systems Our work related toanalysis and proof of formal systems mainly focuses on models inspired byrewriting, and on the verification of hybrid and continuous systems.

The rewriting theory has been developed over the last 30 years by manyresearch teams worldwide. One of our specificities is to focus on rewriting con-trolled by strategies, and in particular on the proof of properties of rewritingsystems under strategies. We have developed inductive approaches for that, inclose relation with some people in the PROTHEO research group with whomwe still collaborate in an active way. In the international community, we canmention some teams in Aachen, Germany, in Valencia, Spain, and in Urbana,Illinois, which are also working on rewriting proof tools for programming.

Our work related to the verification of hybrid and continuous systems isclose to problems under study in the model checking community. Many re-search teams focus worldwide on verification or on the control theory of hybridsystems, as can be measured by the Hybrid Systems Computation and Control,or the Conference on Decision and Control conference series. In particular, inthe French world, we can mention some teams in LIAFA in Paris VII, in LSVin Cachan, in IRISA in Rennes, in VERIMAG in Grenoble, LORIA in Nancy.

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Compared to more common approaches, we focus on complexity or computabil-ity theoretic related questions, and we collaborate with several people of theseteams about such questions.

On implicit computational complexity, there are several teams with slightlydifferent directions. Martin Hofmann in Munich develops type systems. Karl-Heinz Niggl uses matrix algebras in Ilmenau. There are several group whichwork on light linear logic : P. Baillot (Paris 13), S. Ronchi della Rocca (U.Turin), . . . In north America, Stephen Cook, Daniel Leivant, Harry Mairson,Jim Royer are well known people who are very active on this field.

Computer Virology Even if it is surprising, there are very few academicworks. Of course, anti-virus companies should do research on this subject, aswell as military labs all over the world. However, there are about twenty paperswhich consider computer virology from a scientific point of view and which areavailable. Most of the papers are about description of viruses or worms whichare published on blogs. Our research is made in strong ties with Eric Filiol(ESAT) and we are starting to collaborate with the University of Luxembourg,of Athens and of Milano. Moreover, we try to federate effots with the TCVconference initiative.

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Project’s bibliography

PhD and ”Habilitations a diriger des recherches”

From 2000

[1] Jerome Besombes. Un modele algorithmique de la generalisation de struc-tures dans le processus d’acquisition du langage. PhD thesis, UniversiteNancy 1, Dec 2003.

[2] Guillaume Bonfante. Construction d’ordres, analyse de la complexite. PhDthesis, INPL, 2000.

[3] Paulin Jacobe de Naurois. Resultats de Completude et Caracterisations Syn-taxiques de Classes de Complexite sur des Structures Arbitraires. PhD thesis,INPL and City university (Hong-Kong), Dec 2004. Joint thesis.

[4] Olivier Fissore. Terminaison de la reecriture sous strategies. Thesed’universite, UHP Nancy I, Dec 2003.

[5] Liliana Ibanescu. Programmation par regles et strategies pour la generationautomatique de mecanismes de combustion d’hydrocarbures polycycliques.These de Doctorat d’Universite, Institut National Polytechnique de Lor-raine, Nancy, France, June 2004.

[6] J.-Y. Marion. Complexite implicite des calculs, de la theorie a la pratique.Habilitation a diriger les recherches, Universite Nancy 2, 2000.

[7] Jean-Yves Moyen. Analyse de la complexite et transformation de pro-grammes. PhD thesis, Universite Nancy 2, 2003.

9.3 Books, scientific edition

From 2000

[1] Jean-Yves Marion. Editorial : Implicit computational complexity (icc).Theoretical Computer Science, 318(1-2):1, Jun 2004. Editeur scientifiqueinvite.

Articles in international journals

From 2000

[1] Lali Barriere, Johanne Cohen, and Margarita Mitjana. Gossiping in chordalrings under the line model. Theoretical Computer Science, 264(1):53–64,2001.

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[2] Dominique Barth, Pascal Berthome, and Johanne Cohen. The eulerianstretch of a digraph and the ending guarantee of a convergence routing.Journal of Interconnection Networks (JOIN), 5(2):93–109, jun 2004.

[3] Dominique Barth, Johanne Cohen, and Corentin Durbach. Multicasttree allocation algorithms for distributed interactive simulation. Inter-national Journal of High Performance Computing and Networking - IJH-PCN., 4(3/4):137–151, 2006.

[4] Dominique Barth, Johanne Cohen, and Touafik Faik. On the b-continuityproperty of graphs. Discrete Applied Mathematics, 2006.

[5] Dominique Barth, Johanne Cohen, Lynda Gastal, Thierry Mautor, andSetephane Rousseau. A comparison of splittable and non-splittable packetmodels in an optical ring network. Journal of Optical Networking (JON),2006.

[6] Jerome Besombes and Jean-Yves Marion. Learning tree languages frompositive examples and membership queries. Theoretical Computer Science,2006.

[7] Vincent Blondel, Olivier Bournez, Pascal Koiran, Christos Papadimitriou,and John Tsitsiklis. Deciding stability and mortality of piecewise affinedynamical systems. Theoretical Computer Science A, 1–2(255):687–696,2001.

[8] Vincent D. Blondel, Olivier Bournez, Pascal Koiran, and John Tsitsiklis.The stability of saturated linear dynamical systems is undecidable. Journalof Computer and System Science, 62(3):442–462, May 2001.

[9] G. Bonfante, A. Cichon, J.-Y. Marion, and H. Touzet. Algorithms withpolynomial interpretation termination proof. Journal of Functional Pro-gramming, 11(1):33–53, 2001.

[10] Guillaume Bonfante, Matthieu Kaczmarek, and Jean-Yves Marion. Onabstract computer virology: from a recursion-theoretic perspective. Journalof computer virology, 1(3-4), 2006.

[11] Guillaume Bonfante, Jean-Yves Marion, and Jean-Yves Moyen. Quasi-interpretations, a way to control resources. Theoretical Computer Science,(revision).

[12] O. Bournez, F. Cucker, P.J. de Naurois, and J.Y. Marion. Implicit com-plexity over an arbitrary structure: Quantifier alternations. Informationand Computation, 204(2):210–230, Feb 2006.

[13] Olivier Bournez. How much can analog and hybrid systems be proved(super-)turing. Applied Mathematics and Computation, 2005. To appear.

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[14] Olivier Bournez and Michael Branicky. The mortality problem for matricesof low dimensions. Theory of Computing Systems, 35(4):433–448, Jul-Aug2002.

[15] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Implicit complexity over an arbitrary structure: Sequential andparallel polynomial time. Journal of Logic and Computation, 15:41–58,2005.

[16] Olivier Bournez and Emmanuel Hainry. Elementarily computable functionsover the real numbers and R-sub-recursive functions. Theoretical ComputerScience, 348(2–3):130–147, 2005.

[17] Olivier Bournez and Emmanuel Hainry. Recursive analysis characterizedas a class of real recursive functions. Fundamenta Informaticae, 2006. Toappear.

[18] Thierry Chich, Johanne Cohen, and Pierre Fraignaud. Unslotted deflectionrouting: a practical and efficient protocol for multi-hop optical networks.IEEE/ACM Transaction on Networking, 9(1):47–58, 2001.

[19] Johanne Cohen, Pierre Fraignaud, and Cyril Gavoille. Recognizing knodelgraphs. Discrete Mathematics, 250:41–62, Mar 2002.

[20] Johanne Cohen, Pierre Fraignaud, and Margarita Mitjana. Polynomialtime algorithms for minimum-time broadcast in tree. Theory of ComputingSystems, 35(6):641–665, 2002.

[21] Johanne Cohen, Emmanuel Jeannot, Nicolas Padoy, and Frederic Wagner.Message scheduling for parallel data redistribution between clusters. IEEETransactions on Parallel and Distributed Systems., 2006.

[22] Serge Grigorieff and Jean-Yves Marion. Kolmogorov complexity and non-determinism. Theor. Comput. Sci., 271(1-2):151–180, 2002.

[23] D. Leivant and J.-Y. Marion. A characterization of alternating log time byramified recurrence. Theoretical Computer Science, 236(1-2):192–208, Apr2000.

[24] Jean-Yves Marion. Analysing the implicit complexity of programs. Infor-mation and Computation, 183(1):2–18, 2003.

Publications in international conferences and workshop

From 2000

[1] Eugene Asarin, Olivier Bournez, Thao Dang, and Oded Maler. Approxi-mate reachability analysis of piecewise-linear dynamical systems. In HybridSystems : Computation and Control (HSCC’00), Pittsburgh (USA), volume

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1790 of Lecture Notes in Computer Science, pages 20–31. Springer-Verlag,March 2000.

[2] Eugene Asarin, Olivier Bournez, Thao Dang, Oded Maler, and Amir Pnueli.Effective synthesis of switching controllers for linear systems. Proceedings ofthe IEEE, Special Issue on ”Hybrid Systems”, 88(7):1011–1025, July 2000.

[3] Dominique Barth, Johanne Cohen, Alain Denise, and Romain Riviere.Shuffling biological sequencess with motifs constraints. In Algorithmsand Computational Methods for Biochemical and Evolutionary Networks(Compbionet 04). KCL publications, 2004.

[4] Dominique Barth, Johanne Cohen, Paraskevi Fragopoulou, and GerardHebuterne. Wavelengths assignment on a ring all-optical metropolitanarea network. In 3rd Workshop on Approximation and RandomizationAlgorithms in Communication Networks - ARACNE’2002, Rome, Italy,September 2002.

[5] Dominique Barth, Johanne Cohen, Lynda Gastal, Thierry Mautor, andStephane Rousseau. Comparison of fixed size and variable size packet mod-els in an optical ring network: Algorithms and performances. In Photonicsin Switching (PS’2003), pages 89–91, 2003.

[6] Dominique Barth, Johanne Cohen, Lynda Gastal, Thierry Mautor, andStephane Rousseau. Fixed size and variable size packet models in an opticalring network: Complexity and simulations. In Cevdet Aykanat, TugrulDayar, and Ibrahim Korpeoglu, editors, 19th International Symposium onComputer and Information Sciences (ISCIS), volume 3280 of Lecture Notesin Computer Science, pages 238–246. Springer, Oct 2004.

[7] Emmanuel Beffara, Olivier Bournez, Hassen Kacem, and Claude Kirchner.Verification of timed automata using rewrite rules and strategies. In SixthAnnual Workshop of the ERCIM Working Group on Constraints, Prague,June 18–20, 2001.

[8] Emmanuel Beffara, Olivier Bournez, Hassen Kacem, and Claude Kirch-ner. Verification of timed automata using rewrite rules and strategies. InNachum Dershowitz and Ariel Frank, editors, Proceedings BISFAI 2001,Seventh Biennial Bar-Ilan International Symposium on the Foundations ofArtificial Intelligence, Ramat-Gan, Israel, June 25–27, 2001.

[9] Jerome Besombes and Jean-Yves Marion. Identification reversible depen-dency tree languages. In 3rd Learning Language in Logic (LLL) Workshop.L. Popelinsky, Matthieu Nepil, Sep 2001.

[10] Jerome Besombes and Jean-Yves Marion. Learning dependency languagesfrom a teacher. In 9th conference on Formal Grammar, Aug 2004.

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[11] Jerome Besombes and Jean-Yves Marion. Learning regular trees withqueries. In Mieczyslaw A. Klopotek, Slawomir T. Wierzchon, and KrzsztofTrojanowski, editors, Intelligent Information Processing and Web Mining,Proceedings of the International IIS : IIPWMO04, Advances in Soft Com-puting, pages 181–190. Springer, May 2004.

[12] Jerome Besombes and Jean-Yves Marion. Learning reversible categorialgrammars from structures. In Categorial Grammars, Jun 2004.

[13] Jerome Besombes and Jean-Yves Marion. Learning tree languages frompositive examples and membership queries. In Shai Ben-David, John Case,and Akira Maruoka, editors, 15th international conference on AlgorithmicLearning Theory - ALT’2004, volume 3244 of Lecture notes in ArtificialIntelligence, pages 440–453. Springer, Oct 2004.

[14] Vincent D. Blondel, Olivier Bournez, Pascal Koiran, and John N. Tsitsik-lis. The stability of saturated linear dynamical systems is undecidable. InHorst Reichel Sophie Tison, editor, Symposium on Theoretical Aspects ofComputer Science (STACS), Lille, France, volume 1770 of Lecture Notes inComputer Science, pages 479–490. LIFL, Springer-Verlag, February 2000.

[15] Guillaume Bonfante, Jean-Yves Marion and Romain Pechoux A Charac-terization of Alternating Log Time by First Order Functional Programs. InLpar 06, Volume 4246 of Lecture Notes in Computer Science, pages 90–104,Springer, 2006.

[16] G. Bonfante, R. Kahle, J-Y Marion and I. Oitavem Towards an implicitcharacterization of NCk In CSL, Volume 4207 of Lecture Notes in ComputerScience, pages 212-224, Springer, 2006.

[17] Guillaume Bonfante. Some programming languages for logspace andptime. In AMAST ’06. Lecture Notes in Computer Science, July 2006.

[18] Guillaume Bonfante, Matthieu Kaczmarek, and Jean-Yves Marion. Towardan abstract computer virology. In ICTAC’05, Lecture Notes in ComputerScience. Springer, Oct 2005.

[19] Guillaume Bonfante, Jean-Yves Marion, and Jean-Yves Moyen. On lexico-graphic termination ordering with space bound certifications. In A. ZamulinD. Bjorner, Matthieu Broy, editor, International Andrei Ershov MemorialConference - PSI’01, volume 2244 of Lecture notes in Computer Science,pages 482–493. Springer, 2001.

[20] Guillaume Bonfante, Jean-Yves Marion, and Jean-Yves Moyen. On com-plexity analysis by quasi-interpretation. In 2nd Appsem II workshop -APPSEM’04, pages 85–95, Apr 2004.

[21] Guillaume Bonfante, Jean-Yves Marion, and Jean-Yves Moyen. Quasi-interpretations and small space bounds. In Jurgen Giesl, editor, Term

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Rewriting and Applications, 16th International Conference, RTA 2005,Nara, Japan, April 19-21, 2005, Proceedings, volume 3467 of Lecture Notesin Computer Science, pages 150–164. Springer, 2005.

[22] Guillaume Bonfante, Jean-Yves Marion, Jean-Yves Moyen, and R. Pe-choux. Synthesis of quasi-interpretations. In LCC, 2005.

[23] Olivier Bournez. A generalization of equational proof theory? In HolgerHermanns and Roberto Segala, editors, Process Algebra and ProbabilisticMethods : Performance Modeling and Verification, volume 2399 of LectureNotes in Computer Science, pages 208–209. Springer-Verlag, July 25–262002.

[24] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Computability over an arbitrary structure. sequential and parallelpolynomial time. In Andrew D. Gordon, editor, Foundations of SoftwareScience and Computational Structures, 6th International Conference (FOS-SACS’2003), volume 2620 of Lecture Notes in Computer Science, pages185–199, Warsaw, 2003. Springer.

[25] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Safe recursion over an arbitrary structure: Par, ph and dph. InAnuj Dawar, editor, Fifth International Worshop on Implicit Computa-tional Complexity - ICC’2003, volume 90 of Electronic Notes in TheoreticalComputer Science, Ottawa, Canada, 2003. Elsevier.

[26] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Tailoring recursion to characterize non-deterministic complex-ity classes over arbitrary structures. In In 2nd APPSEM II Workshop(APPSEM’04), April 2004.

[27] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Tailoring recursion to characterize non-deterministic complexityclasses over arbitrary structures. In 3rd IFIP International Conference onTheoretical Computer Science - TCS’2004, Toulouse, France, August 2004.Kluwer Academic Press.

[28] Olivier Bournez, Felipe Cucker, Paulin Jacobe de Naurois, and Jean-YvesMarion. Logical characterizations of pK and npK over an arbitrary structurek. 2005.

[29] Olivier Bournez, Guy-Marie Come, Valerie Conraud, Helene Kirchner, andLiliana Ibanescu. Automated generation of kinetic chemical mechanismsusing rewriting. In P.M.A. Sloot, D. Abramson, A.V. Bogdanov, J.J. Don-garra, A.Y. Zomaya, and Y.E. Gorbachev, editors, International Confer-ence on Computational Science - ICCS 2003, Melbourne, June 2-4, 2003,Proceedings, Part III, volume 2659 of Lecture Notes in Computer Science,pages 367–376. Springer, 2003.

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[30] Olivier Bournez, Guy-Marie Come, Valerie Conraud, Helene Kirchner, andLiliana Ibanescu. A rule-based approach for automated generation of ki-netic chemical mechanisms. In Robert Nieuwenhuis, editor, Rewriting Tech-niques and Applications, 14th International Conference, RTA 2003, Valen-cia, Spain, June 9-11, 2003, Proceedings, volume 2706 of Lecture Notes inComputer Science, pages 30–45. Springer, June 2003.

[31] Olivier Bournez, Paulin de Naurois, and Jean-Yves Marion. Safe recur-sion and calculus over an arbitrary structure. In Implicit ComputationalComplexity - ICC’02, Copenhagen, Denmark, July 2002.

[32] Olivier Bournez and Florent Garnier. Proving positive almost sure termi-nation. In Jurgen Giesl, editor, 16th International Conference on RewritingTechniques and Applications (RTA’2005), volume 3467 of Lecture Notes inComputer Science, page 323, Nara, Japan, 2005. Springer.

[33] Olivier Bournez, Mohamed El Habib, Claude Kirchner, Helene Kirch-ner, Jean-Yves Marion, and Stephan Merz. The qsl plateform atloria. In First QPQ Workshop on Deductive Software Components,pages 9–12, Miami, Florida, July 28 2003. CADE-19 Workshop,ftp://ftp.csl.sri.com/pub/users/shankar/QPQ03.pdf, file = ”perso.bib”.

[34] Olivier Bournez and Emmanuel Hainry. An analog characterization of el-ementarily computable functions over the real numbers. volume 3142 ofLecture Notes in Computer Science, pages 269–280, Turku, Finland, 2004.Springer.

[35] Olivier Bournez and Emmanuel Hainry. An analog characterization of ele-mentarily computable functions over the real numbers. In In 2nd APPSEMII Workshop (APPSEM’04), Tallinn, Estonia, April 2004.

[36] Olivier Bournez and Emmanuel Hainry. Real recursive functions and realextentions of recursive functions. In Maurice Margenstern, editor, Ma-chines, Computations and Universality (MCU’2004), volume 3354 of Lec-ture Notes in Computer Science, Saint-Petersburg, Russia, September 2004.

[37] Olivier Bournez and Mathieu Hoyrup. Rewriting logic and probabilities. InRobert Nieuwenhuis, editor, Rewriting Techniques and Applications, 14thInternational Conference, RTA 2003, Valencia, Spain, June 9-11, 2003,Proceedings, volume 2706 of Lecture Notes in Computer Science, pages 61–75. Springer, June 2003.

[38] Olivier Bournez, Liliana Ibanescu, and Helene Kirchner. From chemicalrules to term rewriting. In 6th International Workshop on Rule-Based Pro-gramming, Nara, Japan, April 2005.

[39] Olivier Bournez and Claude Kirchner. Probabilistic rewrite strategies: Ap-plications to ELAN. In Sophie Tison, editor, Rewriting Techniques andApplications, volume 2378 of Lecture Notes in Computer Science, pages252–266. Springer-Verlag, July 22-24 2002.

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[40] Olivier Bournez and Oded Maler. On the representation of timed polyhe-dra. In International Colloquium on Automata Languages and Program-ming (ICALP’00), volume 1853 of Lecture Notes in Computer Science,pages 793–807, Geneva, Switzerland, 9–15 July 2000. Springer.

[41] Johanne Cohen, Fedor Fomin, Pinar Heggernes, Dieter Kratsch, and Gre-gory Kucherov. Optimal linear arrangement of interval graphs. In Springer-Verlag, editor, 31st International Symposium on Mathematical Foundationsof Computer Science - MFCS 2006, Lecture Notes in Computer Science,pages 267–279, 2006.

[42] O. Fissore, I. Gnaedig, and H. Kirchner. Termination of rewriting with localstrategies. In M. P. Bonacina and B. Gramlich, editors, Selected papersof the 4th International Workshop on Strategies in Automated Deduction,volume 58 of Electronic Notes in Theoretical Computer Science. ElsevierScience Publishers B. V. (North-Holland), 2001.

[43] O. Fissore, I. Gnaedig, and H. Kirchner. CARIBOO : An induction basedproof tool for termination with strategies. In Proceedings of the FourthInternational Conference on Principles and Practice of Declarative Pro-gramming, pages 62–73, Pittsburgh (USA), October 2002. ACM Press.

[44] O. Fissore, I. Gnaedig, and H. Kirchner. Outermost ground termination. InProceedings of the Fourth International Workshop on Rewriting Logic andIts Applications, volume 71 of Electronic Notes in Theoretical ComputerScience, Pisa, Italy, September 2002. Elsevier Science Publishers B. V.(North-Holland).

[45] O. Fissore, I. Gnaedig, and H. Kirchner. Simplification and termination ofstrategies in rule-based languages. In Proceedings of the Fifth InternationalConference on Principles and Practice of Declarative Programming, pages124–135, Uppsala (Sweden), August 2003. ACM Press.

[46] O. Fissore, I. Gnaedig, and H Kirchner. A proof of weak termination provid-ing the right way to terminate. In First International Colloquium on The-oretical Aspect of Computing, volume 3407 of Lecture Notes in ComputerScience, pages 356–371, Guiyang, China, September 2004. Springer-Verlag.

[47] Olivier Fissore, Isabelle Gnaedig, and Helene Kirchner. CARIBOO: Amulti-strategy termination proof tool based on induction. In Albert Rubio,editor, Proceedings of the 6th International Workshop on Termination 2003,pages 77–79, Valencia (Spain), June 2003.

[48] Pascal Fontaine, Jean-Yves Marion, Stephan Merz, Leonor Prensa Nieto,and Alwen Tiu. Expressiveness + automation + soundness: Towards com-bining smt solvers and interactive proof assistants. In TACAS, LectureNotes in Computer Science. Springer, 2006.

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[49] I. Gnaedig and H. Kirchner. Termination of rewriting strategies: a genericapproach. In H.-W. Loidl M. Hofmann, editor, APPSEM II Workshop 2005,Chiemsee, Germany, September 2005. APPSEM II & Ludwig MaximiliansUniversitat Munchen.

[50] I. Gnaedig and H. Kirchner. Computing Constructor Forms with Non Ter-minating Rewrite Programs. In Proceedings of the Eighth ACM-SIGPLANInternational Symposium on Principles and Practice of Declarative Pro-gramming, pages 121–132, Venice, Italy, July 2006. ACM.

[51] H Kirchner and I. Gnaedig. Termination and normalisation under strategy- Proofs in ELAN. In Proceedigs of the Third International Workshop onRewriting Logic and its Applications, volume 36 of Elecronic Notes In The-oretical Computer Science, Kanazawa, JAPAN, September 2000. ElsevierScience Publishers B. V. (North-Holland).

[52] J.-Y. Marion and J.-Y. Moyen. Efficient first order functional programinterpreter with time bound certifications. In Michel Parigot and AndreiVoronkov, editors, Logic for Programming and Automated Reasoning, 7thInternational Conference, LPAR 2000, Reunion Island, France, volume1955 of Lecture Notes in Computer Science, pages 25–42. Springer, Nov2000.

[53] J-Y Marion and R. Pechoux. Resource analysis by sup-interpretation. InFLOPS, volume 3945 of Lecture Notes in Computer Science, pages 163–176.Springer, 2006.

[54] Jean-Yves Marion. Actual arithmetic and feasibility. In L. Fribourg, editor,International Workshop on Computer Science Logic - CSL’2001, volume2142 of Lecture notes in Computer Science, pages 115–129. Springer, Sep2001.

Articles in national journals

From 2000

[1] Anne Bonfante and Jean-Yves Marion Les paradoxes de la defense virale :la cas Bradley Misc, Volume 28, pages 4–7, 2006

[2] Jerome Besombes and Jean-Yves Marion. Apprentissage des langagesreguliers d’arbres et applications. Traitement automatique de langues,44(1):121–153, Jul 2003.

[3] Guillaume Bonfante, Bruno Guillaume, and Guy Perrier. Analyse syntaxiqueelectostatique. Traitement Automatique des Langues, 44:3 Evolutions enanalyse syntaxique, 2003.

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Publications national conference and workshop

From 2000

[1] Henry Amet, Johanne Cohen, Freddy Deppner, Marie-Claude Portmann,and Stephane Rousseau. Un probleme d’ordonnancement de messages : Par-tie 1 modelisations. In 6eme congres de la Societe Francaise de RechercheOperationnelle et d’Aide a la Decision (ROADEF), pages 54–55, 2005.

[2] Henry Amet, Johanne Cohen, Freddy Deppner, Marie-Claude Portmann,and Stephane Rousseau. Un probleme d’ordonnancement de messages : Par-tie 2 approches de resolution. In 6eme congres de la Societe Francaise deRecherche Operationnelle et d’Aide a la Decision (ROADEF), pages 56–57,2005.

[3] Dominique Barth, Johanne Cohen, and Corentin Durbach. Algorithmes derepartition de charge pour des simulations distribuees. In 5ieme congres dela Societe Francaise de Recherche Operationnelle et d’Aide a la Decision(ROADEF 2003), pages 55–56, 2003.

[4] Jerome Besombes and Jean-Yves Marion. Apprentissage des langagesreguliers d’arbres et applications. In Conference d’Apprentissage -CAP’2002, pages 55–70, Jul 2002.

[5] Jerome Besombes and Jean-Yves Marion. Apprentissage des langagesreguliers d’arbres a l’aide d’un expert. In Conference d’Apprentissage -CAP’2003, Jul 2003.

[6] Jerome Besombes and Jean-Yves Marion. Apprentissage des grammairescategorielles a partir de structures. In Conference Francophone dAppren-tissage - CAp’2004, pages 315–330. Presse universitaire de Grenoble, Jun2004.

Patents

From 2000

[1] O. Fissore, I. Gnaedig, and H Kirchner. Cariboo, a termi-nation proof tool for rewriting-based programming languages withstrategies, Version 1.0. Free GPL Licence, APP registrationIDDN.FR.001.170013.000.R.P.2005.000.10600, August 2004.

[2] O. Fissore, I. Gnaedig, H. Kirchner, and L. Moussa. Cariboo,a termination proof tool for rewriting-based programming languageswith strategies, Version 1.1. Free GPL Licence, APP registrationIDDN.FR.001.170013.000.S.P.2005.000.10600, December 2005. Availableat http://protheo.loria.fr/softwares/cariboo/.

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Technical reports

From 2000

[1] Dominique Barth, Johanne Cohen, and Touafik Faik. Complexity of deter-mining the b-continuity property of graphs. Technical Report RR-2003/37,PRiM, Universite Versailles, 2003.

[2] Dominique Barth, Johanne Cohen, and Touafik Faik. Non approximabilityand non-continuity of the fall coloring problem. Technical report, LRI, 2005.

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The permanent members, in brief

• Guillaume Bonfante has been Maıtre de Conferences at the Ecole Na-tionale Superieure des Mines de Nancy - INPL since 2001. He defendedhis PhD in 2000 with Adam Cichon. He is working in the Calligrammeresearch group, and is currently in detachment at INRIA. His research in-terests are essentially complexity and resource analysis. He is now tacklingthe theory of viruses.

• Olivier Bournez is Charge de Recherche at INRIA in Protheo researchgroup. After Ecole Normale Superieure de Lyon where he defended hisPhD with Michel Cosnard on the algorithmic complexity of continuousand dynamic systems in 1999, he spent one year in the Verimag labora-tory in Grenoble. His research interests include computability and com-plexity theory of continuous models, verification of continuous and hybridsystems, theory and algorithmic of systems with probabilistic aspects, dis-tributed algorithmic, and incentive algorithmic.

• Johanne Cohen is Chargee de Recherche at CNRS. After Ecole NormaleSuperieure de Lyon, where she defended her PhD with Pierre Fraigniaudin 1998 about group communications in the line model, she was ATERat Parix XI University. She then got a Maitre de Conference positionin Nancy in 2000, and then the Charge de Recherche position at CNRSin 2001. Her research interests include distributed algorithmics, incen-tive algorithmics, and in particular algorithmics for telecommunicationsnetworks.

• Isabelle Gnaedig is Chargee de Recherche at INRIA in Protheo re-search group. After studies in mathematics and computer science, shedefended her PhD about the termination of rewriting with associative-commutative axioms with Pierre Lescanne in 1986. She obtained herChargee de Recherche position at INRIA at the end of 1986. Between1987 and 1997, she was in charge of promotion and communication of theCentre de Recherche en Informatique de Nancy and of the INRIA-Lorraineresearch unit. Doing research at full time since 1998, she is interested inautomated deduction, rule-based programming and termination.

• Jean-Yves Marion has been Professeur at the Ecole Nationale Superieuredes Mines de Nancy - INPL since 2002. He defended his PhD in 1992 withSerge Grigorieff, at the Paris 7 University (LITP), about the complexityof the T system of Godel interpreted on finite structures. He spent twoyears at the University of Indiana to work with Daniel Leivant. His firstresearch subject is about computer security and is based on three issues:(i) controlling resources, (ii) computer virology, (iii) the cooperation of de-duction tools. The second is about learning (grammatical inference) andthe theory of information (Kolmogorov complexity).

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