Direction des Relations Internationales (DRI)

Programme INRIA "Equipes Associées"
(Demande de prolongation)

 

I. DEFINITION

EQUIPE ASSOCIEE

DST : Distributed systems,  Supervision and Time.

sélection

 2009

 

Equipe-Projet INRIA : Distribcom & S4

Organisme étranger partenaire : National University of Singapore

Organisme étranger partenaire : Chennai Mathematical Institute and Institute for Mathematical Science.

Centre de recherche INRIA : INRIA Rennes Bretagne Atlantique

Thème INRIA : Réseaux, systèmes et services, calcul distribué – Réseaux et télécommunications.

 

&

 

Algorithmique, programmation, logiciels et architectures – Systèmes embarqués et temps réel.

Pays : SINGAPORE

Pays : INDIA

 

 

Coordinateur français

Coordinateur étranger

Coordinateur étranger

Nom, prénom

 Hélouët, Loïc

 P.S. Thiagarajan

Madhavan Mukund

Grade/statut

 CR1

 Professor

Professor

Organisme d'appartenance
(précisez le département et/ou le laboratoire)

 INRIA Rennes, Bretagne Atlantique

Equipe Distribcom

 National University of Singapore (NUS)

Chennai Mathematical Institute

Adresse postale

 IRISA,

Campus de Beaulieu,

35042 Rennes Cedex,

France

 School of Computing
National University of Singapore
Computing 1
13 Computing Drive
Singapore 117417
Republic of Singapore

Chennai Mathematical Institute
Plot H1, SIPCOT IT Park
Padur PO, Siruseri 603103
India

 

URL

 http://www.irisa.fr/distribcom/Personal_Pages/helouet/newloic.html

 http://www.comp.nus.edu.sg/~thiagu/

http://www.cmi.ac.in/~madhavan/

Téléphone

 33 2 99 84 75 90

 +65 6874 7998

+91 44 2747 0226-0229

Télécopie

 33 2 99 84 71 71

 

+91 44 2747 0225

Courriel

 Loic.helouet@irisa.fr

 thiagu@comp.nus.edu.sg

madhavan@cmi.ac.in

NOTA : Si la proposition d'Equipe Associée comporte plusieurs partenaires, français et/ou étrangers, vous pouvez :
- soit ajouter une colonne,
- soit dupliquer le tableau ci-dessus autant de fois que nécessaire, en remplaçant "Coordinateur français ou étranger" par "Autre participant français ou étranger".


La proposition en bref

Titre de la thématique de collaboration (en français et en anglais) : DST  - Distributed systems : Supervision and Time

Descriptif (environ 10 lignes) : This associated team is a tripartite collaboration between two projects at INRIA Rennes (S4 & Distribcom), the National University of Singapore (NUS), and two institutes in Chennai (INDIA), the Chennai Mathematical Institute (CMI) and the Institute of Mathematical Sciences (IMS). The objective of the DST project is to study distributed systems, supervision and time issues with the help of concurrency models. The two main themes of the project are supervision, and quantitative/timed aspects of systems. The supervision theme will focus on distributed scheduling policies of distributed systems to ensure satisfaction of some properties (preservation of some bound on communication channels, for instance), diagnosis, and distributed control techniques. The second theme on time aspects of distributed systems will focus on the analysis of qualitative and quantitative properties of timed systems and models. The quantitative approaches will rely on network calculus applied to multimode Real Time Calculus, and the timed models studied during the collaboration will be inspired from timed scenarios. We expect some interaction between the two themes, that is improve timed characteristics (throughput, …) using supervision techniques, or conversely use some knowledge of time in a system to perform more accurate diagnosis and supervision.

 


II. BILAN 2009

Changements majeurs survenus concernant l'Equipe Associée (modifications des objectifs scientifiques, des chercheurs impliqués)

 

Rapport scientifique de l'année 2009

(joindre la page du programme de travail initialement prévu fin 2008 pour l'année 2009
ou insérer un lien vers cette page)

Description de l'activité scientifique de l'équipe associée et des résultats obtenus : publications, communications, organisation de colloques, formation, soutenances de thèse, valorisation économique, sociale, industrielle, enregistrement de logiciels, dépôt de brevets ... (1 à 2 pages)

This associated team is a tripartite collaboration between two projects at INRIA Rennes (S4 & Distribcom), the National University of Singapore (NUS), and two institutes in Chennai (INDIA), the Chennai Mathematical Institute (CMI) and the Institute of Mathematical Sciences (IMS). The objective of the DST project is to study distributed systems, supervision and time issues with the help of concurrency models. The two main themes of the project are supervision, and quantitative/timed aspects of systems. For a more detailed presentation of the objectives of the associated team, we refer interested readers to the complete description at the following address: http://www.irisa.fr/distribcom/DST09/DSTSoumission2009.html

 

Many fruitful discussions with our Indian and Singaporean partners took place during the first year of the DST project. This led to define research objectives on a smaller set of topics than in the original proposal, focusing on the most promising techniques. These objectives involve two research themes over distributed systems, namely time aspects, and supervision and control aspects. Considering the later, the activities of DST in 2009 have mainly focused on designing distributed controllers, and in particular making the synthesis as small as possible. For the former, activities have focused on network calculus, and on verification of timed MSCs.

 

 

Theme 1 : Supervision and control

 

This theme addresses the problem of  distributed supervisory control, i.e. synthesis of a set of controllers supervising the system in a distributed way, so that the monitored system satisfies some given properties. The particular focus we choose is to minimize the resources needed for the synthesis. For instance, we want to minimize the size of messages, the overall number of messages, and the number of messages in transit at a given time, such that the results we expect to find will be applicable in practice. We did not produce publishable results yet, but we expect to publish some in 2010. We reviewed many different techniques to select the most promising ones: Wonham supervisory control theory [Wonham89], games of imperfect information [Reif79] and Rabin’s Theorem to decide which global configuration can be safely controlled. When the wining set of configurations is known, game theory tells us that for safety objectives, a winning strategy for the controllers is to ensure only that the current configuration is winning. Then, one could use gossiping automata [Mulkun97] obtained with Zielonka theorem or Petri Net synthesis to obtain small controllers staying in safe configurations.

 

Involved researchers :   Rennes : L. Helouet, P.Darondeau, B.Genest,

                        Chennai : M.Mukund, N. Kumar, R. Ramanujam, P.Soumya (PhD), S. Akshay (PhD).

                        Singapore :  P.S. Thiagarajan.

 

Results in 2009:

 

·        Distributed Control of Concurrent Systems: Wonham supervisory control theory for distributed systems is a big challenge due to the partial information each process has on the global configuration of the system. This added to the partial observation each process has already on its local actions in Wonham control theory lead us to use the results obtained for games of imperfect information. One member of DST studied how to synthesize strategies in games with signals, leading to a publication in the LICS conference [BGG09]. In these games, two players have partial and incomparable information about the state of the system. They have antagonistic goals. The aim is to extend these results to more than two players, with two antagonist teams with conflicting goals, but where processes in the same team collaborate. These games have been studied in full generality by [Reif79] but strategy synthesis was shown undecidable. However, distributed games are not as complicated as those studied in [Reif79]. This year, we discussed a particular way of solving games, using Rabin’s Theorem. More precisely, there exists a controller if and only if some logical fomula is satisfied by the behavioural tree of the system. Two results seem promising: first, Rabin’s theorem states that it is decidable whether an MSO formula is satisfied by a regular tree. The second is that the behaviors of distributed  systems can be expressed as a tree. The challenge is that one can define an MSO formula ensuring the existence of a controller on a DAG (the unfolding of the system), or one can define an MSO formula with subtree equivalence on the tree structure. However, decidability of neither of these problems is yet ensured.

 

·        Minimal implementation: This topic is a new problem emerging from the discussions within DST, and addresses the minimal distributed implementation of a global specification. It can be seen as a particular distributed supervision problem. The main objective is to start from a global specification, and to distribute it efficiently on a given architecture (i.e. synthesize a set of communicating machines that preserves the global behaviour of the original specification). Of course, this implementation cannot be a simple projection of the global specification on each site of the architecture, and processes composing the distributed system need some coordination to ensure that the original specification is implemented. Usually, simple parallel composition of the communicating machines obtained via projection of the global specification will allow more behaviors than in the specification. A lot of work has been devoted to finding exact implementations of global specifications (see [Mukund97] for instance). Here, the objective is to study how to implement a global specification on a given architecture when the obtained communicating machines are allowed additional coordination messages that are implementable by the architecture. A solution to this problem proposed in [Genest05] is to implement a leader election protocol among strongly connected components (one process synchronize all the processes in its component), and to overflow messages between connected components. Our goal is to obtain minimal implementation, i.e. using as little messages and synchronization as possible among processes. Study of this problem is still in its infancy, but we expect preliminary result arriving next year, based on Petri net implementation techniques.

 

·        Scheduler ensuring minimal number of messages in transit: Scheduling can be considered as a weakened version of supervisory control, ensuring minimal number of messages in transit by activating processes according to an adequate strategy. The activities around scheduling this year have been a continuation of the former work initiated during the CASDS associated team, focussing on producing distributed schedulers, while the scheduler produced after the CASDS project was global [2].

 

 

 

Theme 2 : Time

 

The second theme addressed by the DST project is time in distributed systems. We want to address time from two points of view. The first one is the study of quantitative aspects, using techniques such as (Max,+) algebra and network calculus, for which both Distribcom and NUS have strong competences. The second aspect is to verify  timed and distributed models, modelled as Message Sequence Charts, a formalism common to several members of Distribcom and of CMI used to describe telecommunication protocols (for which the timing aspect is crucial). The challenge here is to avoid considering every  linearization of the systems to fight the combinatorial explosion (which would lead to inefficiency and worse to undecidability), while time may force the system to follow problematic linearizations.

 

Involved researchers :      Rennes : A. Bouillard, R. Adhami (Master Student), L.Hélouët, B.Genest, G.Aggarwal (Internship)

                                       Chennai : S. Akshay (PhD), M.Mukund, N.K Kumar

                                       Singapore : P.S. Thiagarajan

 

 

Results in 2009:

 

·        Quantitative aspects using simulation : At the occasion of Gunjan Aggarwal’s internship in the Distribcom team this summer, we have developed a simulator for Timed Message Sequence Charts. This simulator takes as input Message Sequence Charts annotated with time, resource consumption and probabilities, transforms the annotated model into a timed, colored and stochastic Petri net, and performs a simulation of this net. The flow of the obtained nets depict the workflow attached to finite (but arbitrarily long) requests arriving in a distributed system. The simulator allows for the simulation of sessions containing up to 10 000 requests, and provides information such as the mean throughput of the system, … It will soon be integrated to the SOFAT Scenario toolbox. 

 

·        Quantitative aspects with nework calculus : During Rami Adhami's master internship, we have studied networks with cyclic dependencies in the Network Calculus framework. In a communication network, several flows circulate and can create cyclic dependences (e.g. there is one flow from node i to node j and one from node j to node i). Deciding whether a given network is stable or not (i.e. at any time the amount of data and the delay of data in the network is bounded by a constant) is an open and difficult problem. Here, we were interested in the stable case and the aim was to compute upper bounds on the maximum transmission delay for a given flow. A first general method using fix-points techniques has been developed, but it gives very loose bounds. A more precise analysis of simple networks (rings) has then been initiated. A promising method is linear programming. The worst-case delay can be computed as the limit of linear programs (with fast convergence), and some methods are still in development to boil down that limit to a single linear program.

 

·        Verification of time constraints for concurrent models: This year, we started investigating properties of Timed Message Sequence Charts, in particular during the visit of S.Akshay at IRISA. This extension proposed by members of DST [AMN07] adds time constraints to Message Sequence Charts (MSCs). This new model also brings several new challenges. For instance, checking time constraints on timed MSCs is an undecidable problem in general, and the only known solution has been to restrict the considered models to the class of regular MSC languages, and to consider every linearization of the system, which is both inefficient and very restrictive. The difficulty is to find a way to verify time constraints over a regular set of representative linearizations, even when the considered model is not regular. In the general case, unbounded MSCs with generic constraints can be used to encode two counter machines, leading to undecidability. We have started investigating some very natural restriction of time constraints which would allow efficient timed model checking, and work for a large class of infinite-state timed systems. Namely, the restrictions we are considering are that the timing constraints shall never force the different processes to drift far away from each other, and the non-zenoness condition, stating that there exists a bound on the number of events forced to be executed in a small amount of time (the constraint can still be compatible with time drifting and non zeno execuctions).

 

Bibliography:

[AMN07] S. Akshay, M. Mukund, K. Narayan Kumar, Checking Coverage for Infinite Collections of Timed Scenarios. CONCUR 2007, p 181-196, 2005.

[BGG09] N. Bertrand, B. Genest, H. Gimbert.   Qualitative Determinacy and Decidability of Stochastic Games with Signals. LICS 2009, p 319-328, 2009.

[Genest05] B. Genest, On Implementation of Global Concurrent Systems with Local Asynchronous Controllers. CONCUR 2005, p 443-45, 2005.

[Mukund97] M. Mukund, M. A. Sohoni,  Keeping Track of the Latest Gossip in a Distributed System. Distributed Computing 10(3), p 137-148, 1997.

[Ramadge89] P.J. Ramadge, W.M. Wonham, The control of discrete event systems, proc. of the IEEE special issue on Dynamics of Discrete Events Systems, 77(1), p 81-98, 1989.

[Reif79] Gary L. Peterson, John H. Reif: Multiple-Person Alternation FOCS 1979: 348-363, 1979.

 

Publications :

[1] T. Gazagnaire, B. Genest, L. Hélouët, P. S. Thiagarajan, S. Yang: Causal Message Sequence Charts. Theoretical  Computer Science 410(41): p 4094-4110, 2009

This publication is a journal version of a work started during the CASDS associated team. It is a special issue of TCS (theoretical Computer Science) journal published at the occasion of Mogens Nielsen’s 60’th birthday.

[2] P. Darondeau, B. Genest, P. S. Thiagarajan, S. Yang: Quasi-Static Scheduling of Communicating Tasks, to appear in Information and Computation., 2009

This publication was selected from a paper accepted at the CONCUR 2008 conference, work done during the CASDS associated team.

[3] Anne Bouillard, Linh T.X. Phan and Samarjit Chakraborty, Functional Modeling of Complex State Dependencies in Stream-Processing Systems, 15th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS 2009).

This work was initiated during the former collaboration within the CASDS associated team.

Software:

A simulator for timed scenarios was developed by G. Aggarwal during her internship in Rennes (from May to July 09). This software starts from scenarios annotated with time, probabilities and resource consumption information, then transforms this input into a colored, timed and stochastic Petri Nets. Traversals of these Petri nets by colored tokens can be seen as requests executions. The software developed allows for the simulation of up to 10 000 simultaneous requests in a reasonable amount of time. It will be shortly integrated to the SOFAT scenario platform.

 

Rapport financier 2009

Avant de remplir les tableaux, consultez les règles au paragraphe "Financement" de la page d'accueil du programme.

 

The invitation line sums up the cost of invitation of S. Akshay (CMI), the internship of G.Aggarwal (this internship was funded by the INRIA internship program, DST only cover travel expenses). The cost of this internship appears as line 1 of the second table. The second line of the second table sums up the cost of missions to Chennai by P.Darondeau and L.Hélouët in January 2009, which were charged to the CASDS associated team.

 

1. Dépenses EA (effectuées sur les crédits de l'Equipe Associée)

Montant dépensé

Invitations des partenaires

  1145,5 (+1000 expected)

Missions INRIA

  3396,60 (+6000 expected)

Total

 4542,1 (+7000 expected)

Justifiez en quelques lignes l'utilisation des crédits et en particulier une utilisation partielle du budget alloué.

2. Dépenses externes (effectuées sur des financements hors EA)

Montant dépensé

Nom de l'organisme 1 (*):INRIA

Invitations des partenaires

  1900

 

Missions INRIA vers le partenaire

 3608,32

 

Total

 5508,32

 

 

(*) Ajouter ou supprimer des lignes au tableau ci-dessus de façon à faire figurer tous les organismes ayant contribué au financement de l'équipe associée

Total des financements externes dépensés

 5508.32

 

Total des financements EA et externes dépensés

10050,42 (+7000 expected)

 

Bilan des échanges effectués en 2009


1. Chercheurs Seniors

The first exchange between INRIA Rennes and Chennai (missions by P. Darondeau and L. Hélouët) were funded by the associated team CASDS, which ended in 2008. We plan two missions to Singapore late November or early December this year.

 

Nom

statut (1)

provenance

destination

objet (2)

durée (3)

Coût (si financement EA)

Coût (si financement externe)

 Darondeau, Philippe

 DR

 Rennes

Chennai

Visit to Chennai Mathematical Institute & Institute for Mathematical Sciences + participation to an Indo-French Workshop on Jan 29-31 

 10 days

 

 1796.07

(EA CASDS – 2006-2008))

 Hélouët, Loïc

 CR1

 Rennes

Chennai

 Visit to Chennai Mathematical Institute & Institute for Mathematical Sciences + participation to an Indo-French Workshop on Jan 29-31 

 10 days

 

 1812.25

(EA CASDS – 2006-2008)

 Genest, Blaise

 CR1

 Rennes

Singapore

Meeting at NUS from 11/02 to 22/02+ partcipation to SINFRA 09 (French/singaporian Workshop) 

 11 days

 3396,60

 

 

 

 

 

 

 

 

 

Genest, Blaise

CR1

Rennes

Singapore

 

10 days

 3000

(to be confirmed)

Hélouët, Loïc

CR1

Rennes

Singapore

 

10 days

 3000

(to be confirmed)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total des durées

 31 days (+ 20 planned at the end of this year

(1) DR / CR / professeur
(2) colloque, thèse, stage, visite....
(3) précisez l'unité (mois, semaine..)


2. Juniors

We have hired an intern student, Mrs Gunjan Aggarwal, to work on simulation of timed scenarios. This internship took place from May 11th to July 24th.

S.Akshay is currently completing a co-supervised PhD between Chennai and Cachan (LSV). We invited him in Rennes, focusing on timed constraints MSC verification.

We have planned to receive the visit of Paul Soumya, a PhD student at IMSC before the end of the year.

Nom

statut (1)

provenance

destination

objet (2)

durée (3)

Coût (si financement EA)

Coût (si financement externe)

 Aggarwal, Gunjan

Internship 

 Guwahati, India

 

Rennes

Internship, from 11/05 to  24/07, financed by the Internship campaign of INRIA

2,5 months

 

1900

 Aggarwal, Gunjan

Internship 

 Guwahati, India

 

Rennes

 Travel expenses

 

 688,23

 

S. Akshay,

 PhD

 Chennai, via Paris

Rennes 

Working meeting

 1 week

 457,27

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Paul Soumya

 PhD

Chennai (IMSC)

Rennes

 

2 weeks

1000

 (to be confirmed)

 

 

 

 

 

 

 

 

 

Total des durées

 2,6 months (+ 2 weeks planned)

(1) post-doc / doctorant / stagiaire
(2) colloque, thèse, stage, visite....
(3) précisez l'unité (mois, semaine..)

III. PREVISIONS 2010

Programme de travail

The proposed work programme can be summarized as follows:

·        Distributed Control of Concurrent Systems: the general case is complicated since routing between processes is arbitrary. We will thus first consider some restricted architecture of communication such as tree structures where the communication is only possible between fathers and sons, but not between siblings or descendant. This should allow us to use concurrent games which are decidable.

·        Minimal Implementation: Now that the minimal implementation is clearly posed, (i.e. find an optimal implementation, with respect to the number of messages, and the number of messages in transit at any time, etc) we are ready to propose algorithmic solutions for the problem. A possible solution may come from Petri net implementation techniques.

·        Quantitative analysis of time: pursue work on quantitative analysis of time for multimode Real Time Calculus with models that are not purely synchronous or asynchronous. Pursue work on bound estimation using the network calculus and linear programming techniques.

·        Timed Scenarios: we will investigate the restrictions on time constraints we came up with in order to verify a large class of communication protocols with timing constraints.

Overall, our aim is to obtain results on open problems which are in the same time effectively usable, and to have them implemented, for instance in our tool SOFAT. Industrial applications could be found among the usual telecommunication partners of the teams Distribcom and S4, Alcatel Lucent and France Telecom. We are currently writing a European IP Proposal called Univerself on self management, in which distributed supervisory control techniques will be used.

Starting from 15 of January 2010, Blaise Genest will be a researcher at UMI IPAL, Singapore, and will work mainly in P.S. Thiagarajan team at NUS.  Though we will consider Blaise Genest as a partner from the singaporian side, we will not use DST funds to cover his visits to Rennes.

  

Programme d'échanges avec budget prévisionnel

1. Echanges

Décrivez les échanges prévus dans les deux sens : invitations de chercheurs de votre partenaire et missions INRIA vers votre partenaire ;
Précisez s'il s'agit de chercheurs confirmés ou de juniors (stagiaires, doctorants, post-doctorants) ;
Motivez, si possible, les raisons scientifiques (travail commun, workshop,..) et précisez la durée prévue ;
Indiquez les étudiants impliqués dans la proposition. Donnez une estimation de leur nombre, pour chaque partenaire, et précisez si des thèses en cotutelle sont prévues ;
Résumez ensuite ces informations dans les tableaux 1 et 2 ci-dessous en faisant une estimation budgétaire :

Visits to Chennai/Singapore

We plan three visits from senior researchers involved in the DST team, plus a visit of a PhD student (that should be hired before the end of 2009 on a bourse de la region Bretagne), who will be working on implementation issues (and hence on the minimal implementation topic in DST). Each of these visits would last between 10 days and two weeks, and will aim at progressing the work on supervision or time aspects mentioned above.

 1. ESTIMATION DES DÉPENSES EN MISSIONS INRIA VERS LE PARTENAIRE

Nombre de personnes

Coût estimé

Chercheurs confirmés

 2

 6000

Post-doctorants

 

 

Doctorants

 1

 2000

Stagiaires

 

 

Autre (précisez) :

 

 

   Total

 2

 8000

 

Visits of Researchers from Chennai/Singapore 

We plan to invite a senior researcher from Chennai or Singapore and devote a large part of the budget to visits of PhD students from Chennai, and to hire an Indian intern during summer 2010.

The intern we hired last year is too young to start a PhD this year, and in our experience, it is hard to convince  English speaking students to come for a Master in France. However, we are asking Ajit Kumar Nema, a student from IIT Delhi who did an internship in 2007 in Rennes on Quasi Static Scheduling (one of the main focus of the previous associated team CASDS) to start a PhD thesis “en cotutelle” between NUS and Rennes. January is the time when positions are opened in NUS.

Moreover, visits of seniors are a good occasion to present research topics of their respective teams. IRISA seniors met Ajay Kattepur, a Master student of Singapore University, in February 2009 during such a visit in Singapore. He is now a PhD student of the Distribcom team (on a subject not covered by the DST team).

 2. ESTIMATION DES DÉPENSES EN INVITATIONS DES PARTENAIRES

Nombre de personnes

Coût estimé

Chercheurs confirmés

 1

3000

Post-doctorants

 

 

Doctorants

 2

3000

Stagiaires

 1

2800

Autre (précisez) :

 

 

   Total

 3

8800

2. Cofinancement

Cette coopération bénéficie-t-elle déjà d'un soutien financier de la part de l'INRIA, de l'organisme étranger partenaire ou d'un organisme tiers (projet européen, NSF, ...) ?
Indiquez ces éléments et donnez les montants associés.

P.S. Thiagarajan has received a 30 000 S$ (approx. 15 000 euros) support from NUS for all the duration of the collaboration.

Both S4 and Distribcom are involved in DISC: Distributed Supervisory Control of Large Plants, an european project of the 7th PCRD that might provide additional financial support for the team, in the supervisory and control theme. DISC will provide 80 k Euros to IRISA in 2010.

Distribcom is involved in DOTS: Distributed, Open and Timed systems, an ANR Security Project. It might provide additional financial support for the team, in the timed and games aspect of the theme. DOTS will provide 33 k Euros to DISTRIBCOM in 2010.

A European IP project Univerself will be soon submitted. If accepted, there would be huge mutual benefit with the Supervision and Control part of DST.

 

3. Demande budgétaire

Indiquez, dans le tableau ci-dessous, le coût global estimé de la proposition et le budget demandé à la DRI dans le cadre de cette Equipe Associée.
(maximum 20 K€ pour une prolongation en 2e année et 10 K€ pour une 3e année).

Commentaires

Montant

A. Coût global de la proposition (total des tableaux 1 et 2 : invitations, missions, ...)

16800

B. Cofinancements utilisés (financements autres que Equipe Associée)

 2000

Financement "Équipe Associée" demandé (A.-B.)
(maximum 20 K€ pour une 2e année et 10 K€ pour une 3e année)

14800

Remarques ou observations :

We have tried to meet the recommendations of the COST during the 2008 evaluation of DST, and to involve more junior researchers. This summer, we have hired an Indian intern (G. Aggarwal, 2,5months) . We also received the visit of S. Akshay (PhD at CMI), and a 2 weeks visit of Paul Soumya (PhD at IMSC) is also expected before the end of the year.

 

 

 

 

 

© INRIA - mise à jour le 08/07/2009