Volumes

This volume contains all the full papers presented at AUTOMATA 2011, the 17th international workshop on cellular automata and discrete complex systems. The workshop was held on November 21-23, 2011, at the Center for Mathematical Modeling, University of Chile, Santiago, Chile.

AUTOMATA is an annual workshop on the fundamental aspects of cellular automata and related discrete dynamical systems. The spirit of the workshop is to foster collaborations and exchanges between researchers on these areas. The workshop series was started in 1995 by members of the Working Group 1.5 of IFIP, the International Federation for Information Processing.

The volume contains the « full » papers selected by the program committee, which consisted of 27 international experts on cellular automata and related models, and the selection was based on 3 peer reviews on each paper.

Papers in this volume represent a rich sample of current research topics on cellular automata and related models. The papers include theoretical studies of the classical cellular automata model, but also many investigations into various variants and generalizations of the basic concept. The versatile nature and the flexibility of the model is evident from the presented papers, making it a rich source of new research problems for scientists representing a variety of disciplines.

As the editors of these proceedings, we thank all contributors to the scientific program of the workshop. We are especially indebted to the invited speakers and the authors of the contributed papers.

Nazim Fatès, Eric Goles, Alejandro Maass, Iván Rapaport

Program Committee

• Andrew Adamatzky, University of West England, UK
• Stefania Bandini, Università degli Studi di Milano-Bicocca, Italy
• Marie-Pierre Béal, Université Paris-Est, France
• Bruno Durand, Université de Provence, France
• Nazim Fatès, Inria Nancy Grand-Est, France, co-chair
• Paola Flocchini, University of Ottawa, Canada
• Enrico Formenti, Université de Nice-Sophia Antipolis, France
• Henryk Fuks, Brock University, Canada
• Anahí Gajardo, Universidad de Concepción, Chile
• Eric Goles, Universidad Adolfo Ibáñez, Chile, co-chair
• Martin Kutrib, University of Giessen, Germany
• Alejandro Maass, Universidad de Chile, co-chair
• Andrés Moreira, Universidad Técnica Federico Santa María, Chile
• Kenichi Morita, Hiroshima University, Japan
• Pedro de Oliveira, Universidade Presbiteriana Mackenzie, Brazil
• Nicolas Ollinger, Université de Provence, France
• Ronnie Pavlov, Denver University, USA
• Marcus Pivato, Trent University, Canada
• Ivan Rapaport, Universidad de Chile, co-chair
• Dipanwita Roychowdhury, Indian Institute of Technology, India
• Mathieu Sablik, Université de Provence
• Michael Schraudner, Universidad de Chile
• Klaus Sutner, Carnegie Mellon, USA
• Guillaume Theyssier, CNRS, Université de Savoie, France
• Edgardo Ugalde, Universidad Autónoma de San Luis Potosí, Mexico
• Hiroshi Umeo, Osaka Electro-Communication University, Japan
• Thomas Worsch, Karlsruhe University, Germany

We were very pleased to receive a record number of submissions this year covering the spectrum of combinatorics and its applications. The presentations will cover many exciting new results and build connections between research areas. We hope you will be able to attend all the lectures and the two poster sessions. We encourage you to ask questions, discuss the material during breaks and participate fully in the FPSAC experience.

Our thanks goes out to everyone attending FPSAC 2010, and especially the members of the Program and Organizing Committees. We also thank the following organizations for their financial support: the National Science Foundation, the National Security Agency, the San Francisco State University College of Science and Engineering and Department of Mathematics, the Fields Institute, Elsevier, and Lindo Systems. Finally, we hope everyone will join us in thanking Federico Ardila and Matthias Beck for taking on the huge job of co-chairing the Organizing Committee.

Sara Billey & Vic Reiner

Program Committee co-chairs

 

Program committee

• Sara Billey (University of Washington, USA, co-chair)
• Vic Reiner (University of Minnesota, USA, co-chair)
• Michael Albert (University of Otago, New Zealand)
• Francesco Brenti (Universita' di Roma "Tor Vergata", Italy)
• Sylvie Corteel (Université Paris XI, France)
• Sergi Elizalde (Dartmouth College, USA)
• Dmitry Feichtner-Kozlov (Universität Bremen, Germany)
• Ira Gessel (Brandeis University, USA)
• Curtis Greene (Haverford College, USA)
• Jim Haglund (University of Pennsilvania, USA)
• Sam Hsiao (Bard College, USA)
• Jakob Jonsson (KTH, Sweden)
• Gil Kalai (Hebrew University, Israel)
• Carly Klivans (University of Chicago, USA)
• Fu Liu (University of California, Davis, USA)
• Soichi Okada (Nagoya University, Japan)
• Julian Pfeifle (Universitat Politècnica de Catalunya, Spain)
• Alexander Postnikov (Massachusetts Institute of Technology, USA)
• David Speyer (Massachusetts Institute of Technology, USA)
• Volkmar Welker (Philipps-Universität Marburg, Germany)
• Alex Yong (University of Illinois at Urbana-Champaign, USA)
• Mike Zabrocki (York University, Canada)

 

• Federico Ardila (San Francisco State University, USA, co-chair)
• Matthias Beck (San Francisco State University, USA, co-chair)
• Nantel Bergeron (York University, Canada)
• Thomas Bliem (San Francisco State University, USA and Universität zu Köln, Germany)
• Tristram Bogart (San Francisco State University, USA and Queen's University, Canada)
• Serkan Hosten (San Francisco State University, USA)
• Brant Jones (University of California, Davis, USA)
• Fu Liu (University of California, Davis, USA)
• Peter McNamara (Bucknell University, USA)
• Ellen Veomett (California State University, East Bay, USA)
• Mike Zabrocki (York University, Canada)

This volume contains the selected "full" papers presented at AUTOMATA 2010, the 16^th inter- national workshop on cellular automata and discrete complex systems. The workshop was held on June 14-16, 2010, at the LORIA laboratory in Nancy, France. AUTOMATA is an annual workshop on the fundamental aspects of cellular automata and related discrete dynamical sys- tems. The spirit of the workshop is to foster collaborations and exchanges between researchers on these areas. The workshop series was started in 1995 by members of the Working Group 1.5 of IFIP, the International Federation for Information Processing. The program committee consisted of 25 international experts on cellular automata and related models, and the selection was based on 2-4 peer reviews on each paper. Papers in this volume represent a rich sample of current research topics on cellular automata and related models. The papers include theoretical studies of the classical cellular automata model, but also many investigations into various variants and generalizations of the basic concept. The versatile nature and the flexibility of the model is evident from the presented papers, making it a rich source of new research problems for scientists representing a variety of disciplines.

As the editors of these proceedings, we thank all contributors to the scientific program of the workshop. We are especially indebted to the invited speakers and the authors of the contributed papers. We would also like to thank the members of the Program Committee and the external reviewers of the papers.

Nazim Fatès, Jarkko Kari, Thomas Worsch

FPSAC 2009 was held at the Research Institute for Symbolic Computation, Hagenberg, Austria, on July 20-24, 2009.
Editors:
Christian Krattenthaler, Volker Strehl, and Manuel Kauers

Preface

This Proceedings volume is devoted to the 21st International Conference on Formal Power Series and Algebraic Combinatorics, held at the Research Institute of Symbolic Computation (RISC) in Hagenberg, Austria, during 20-24 July 2009. The conference was extremely well attended: 200 graduate students, junior researchers, and senior researchers from Austria, Canada, Colombia, China, Czech Republic, Denmark, France, Germany, Greece, Iceland, Israel, Italy, Japan, Mexico, Poland, Portugal, Slovenia, Spain, South Africa, South Korea, Sweden, the United Kingdom, and the United States gathered to enjoy the overwhelming hospitality of the RISC Combinatorics Group.

The conference programme featured nine invited lectures, given by Alexander Barvinok, Karin Erdmann, Jaroslav Nesetril, Bruno Salvy, Carsten Schneider, Michael Singer, Frank Sottile, Volkmar Welker, and Ae Ja Yee, 26 contributed talks, and 48 poster presentations. This volume contains the extended abstracts for most of the contributed papers and poster presentations, all of which had been selected in a careful reviewing process by the programme committee from submissions. These extended abstracts show the wide range of topics presented at the conference, linked together by the overall theme of Formal Power Series and Algebraic Combinatorics. These included enumeration, combinatorial geometry, commutative algebra, algebraic geometry, combinatorial representation theory, Hopf algebras, computational complexity, algebraic graph theory, and, of course (genius loci!), computer algebra. We thank all contributors and participants for having made this conference a show-case of current trends in the field and a lively place of exchange of ideas.

The organizers are very grateful for the financial support of the Johannes Kepler University Linz, the Austrian Science Foundation FWF, the province of Upper Austria, the University Fund Linz (Linzer Hochschulfonds), the Austrian Ministry of Science, the US National Science Foundation (NSF), and the US National Security Agency (NSA). They made it possible, with Susanna Fishel as manager, that a large number of young researchers could profit from this conference, respectively present their work. Funds generously provided by Elsevier were allocated to the Elsevier award for best extended abstract by a student (Guillaume Chapuy).

We would like to thank all of those who served on the Programme and Organising Committees, without whose contribution such a conference could never have been held. Furthermore, the help of Tanja Gutenbrunner, Gabriela Hahn, Veronika Pillwein, Marion Schimpl, and Ralf Hemmecke was more than invaluable to the local organizers.

Manuel Kauers (Scientific Programme Manager)
Christian Krattenthaler (Co-chair, Programme Committee)
Peter Paule (Chair, Organising Committee)
Volker Strehl (Co-chair, Programme Committee)

Committees
Program Committee

• Christian Krattenthaler (Co-Chair; University of Vienna, Austria)
• Volker Strehl (Co-Chair; University of Erlangen, Germany)
• Matthias Beck (San Francisco State University, USA)
• Philippe Caldero (Universite Lyon-I, France)
• Eva-Maria Feichtner (University of Bremen, Germany)
• Sergey Fomin (University of Michigan, USA)
• Jan de Gier (University of Melbourne, Australia)
• Antonio Giambruno (University of Palermo, Italy)
• Takayuki Hibi (University of Osaka, Japan)
• Alain Lascoux (Universite Marne-la-Vallee, France)
• Ezra Miller (University of Minnesota, Minneapolis, USA)
• Maxim Nazarov (University of York, UK)
• Marc Noy (Univ. Politecnica de Catalunya, Barcelona, Spain)
• Grigori Olshanski (Dobrushin Mathematics Laboratory, Moscow, Russia)
• Soichi Okada (University of Nagoya, Japan)
• Marko Petkovsek (University of Ljubljana, Slovenia)
• Amitai Regev (Weizmann Institute, Rehovot, Israel)
• Monica Vazirani (University of California, Davis, USA)
• Michelle Wachs (University of Miami, USA)
• Lauren K. Williams (Harvard University, Boston, USA)
• Catherine Yan (Texas A&M University, USA)

Organizing Committee

• Peter Paule (Chair; RISC, Johannes Kepler University Linz, Austria)
• Susanna Fishel (Arizona State University, USA)
• Ralf Hemmecke (RISC, Johannes Kepler University Linz, Austria)
• Manuel Kauers (RISC, Johannes Kepler University Linz, Austria)
• Franz Lichtenberger (RISC, Johannes Kepler University Linz, Austria)
• Wolfgang Windsteiger (RISC, Johannes Kepler University Linz, Austria)

Local Arrangements Committee

• Veronika Pillwein (Chair; DK Computational Math., Johannes Kepler University Linz, Austria)
• Burcin Erocal (RISC, Johannes Kepler University Linz, Austria)
• Christoph Koutschan (RISC, Johannes Kepler University Linz, Austria)
• Clemens Raab (DK Computational Mathematics, Johannes Kepler University Linz, Austria)
• Silviu Radu (RISC, Johannes Kepler University Linz, Austria)
• Flavia Stan (RISC, Johannes Kepler University Linz, Austria)

 

Bruce Sagan (Michigan State University, USA) (Chair)
Christian Krattenthaler (Universität Wien, Austria) (Co-chair)
Federico Ardila (San Francisco State University, USA)
Jean-Christophe Aval (Université Bordeaux 1, France)
Christine Bessenrodt (Universität Hannover, Germany)
Xun Dong (University of Miami, USA)
Susanna Fishel (Arizona State University, USA)
Sergey Fomin (University of Michigan, USA)
Patricia Hersh (Indiana University, USA)
Ronald King (University of Southampton, UK)
Luc Lapointe (Universidad de Talca, Chile)
Jeremy Lovejoy (Université Denis Diderot, France)
Jeremy Martin (University of Kansas, USA)
Jean-Christophe Novelli (Université de Marne-la-Vallée, France)
Frédéric Patras (Université de Nice, France)
Peter Paule (Universität Linz, Austria)
Nathan Reading (North Carolina State University, USA)
Bruno Salvy (INRIA, France)
Mark Shimozono (Virginia Tech University, USA)
Einar Steingrímsson (Reykjavik University, Iceland)
Itaru Terada (University of Tokyo, Japan) Organizing Committee-Comité d'Organisation Federico Ardila (San Francisco State University, USA)
Hélène Barcelo (Arizona State University, USA)
Christian Krattenthaler (Universität Wien, Austria)
María Ines Icaza (Universidad de Talca, Chile)
Luc Lapointe (Universidad de Talca, Chile) (Chair)
Jennifer Morse (Drexel University, USA)

 

 

This Proceedings volume is devoted to the 20th International Conference on Formal Power Series and Algebraic Combinatorics, held in Viña del Mar, Chile, during 23-27 June 2008. The conference attracted an audience of approximately 120 participants, consisting of graduate students, junior researchers, and senior researchers from Argentina, Australia, Austria, Canada, Chile, Colombia, China, France, Germany, Iceland, Israel, Japan, South Korea, Mexico, New Zealand, Portugal, Russia, Spain, Sweden, the United States and Venezuela.

The conference was dedicated to Pierre Leroux (1942-2008), who, while serving as president of the permanent programme committee of this conference series from 1991 to 1998, has been one of the driving forces which have made this series into the continuing success that it has been over the past 20 years.

The conference programme featured eight invited lectures, given by Marcelo Aguiar, Michael Albert, Jonathan Brundan, Dmitry Feichtner-Kozlov, Gilbert Labelle, Alexander Postnikov, María Ronco, and Carla Savage, 26 contributed talks, and 39 poster presentations. This volume contains the extended abstracts for most of the contributed talks and poster presentations, all of which had been selected in a careful reviewing process by the programme committee from submissions. These extended abstracts reflect the thematic breadth of the conference by covering aspects of Formal Power Series and Algebraic Combinatorics, including enumeration, commutative algebra, algebraic geometry, combinatorial representation theory, Hecke algebras, Hopf algebras, computational complexity, and statistical physics. We thank all contributors and participants for having made this conference a show-case of current trends in the field and a lively place of exchange of ideas.

The organizers are very grateful for the financial support of the Universidad de Talca (through funds from the Dirección de Investigación y Asistencia Técnica and the Instituto de Matemáticas) and of the Programa Bicentenario de Ciencia y Tecnología: Anillo Ecuaciones Asociadas a Reticulados (Chile). Many American participants were given the opportunity to attend the conference thanks to the support of the National Science Foundation and the National Security Agency. The Fields Institute was very helpful in managing the registration process, and funds generously provided by Elsevier were allocated to the Elsevier award for best extended abstract by a student (Valentin Féray) and to the support of Latin American participants.

We would like to thank all of those who served on the Programme and Organizing Committees, whitout whose contribution such a conference could never have been held. Finally, the help of Ricardo Baeza, Andrés Bustamante, Erdal Emsiz, Raimundo Hamilton, Ana Cecilia de la Maza, María Elena Pinto, Nancy Ruminot, Steen Ryom-Hansen, and especially Blanca Zúñiga, was more than invaluable to the local organizers.

Christian Krattenthaler
Luc Lapointe
Bruce Sagan

The Fifth Colloquium on Mathematics and Computer Science is, singularly, the sixth one in a series of events that began at the University of Versailles Saint-Quentin with the Colloque Arbres in June 1995, then went on to the First and Second Colloquia on Mathematics and Computer Science in September 2000 and 2002, again in Versailles, the third edition being hold in Vienna in 2004 and the fourth in Nacy 2006. These meetings aim try provide a forum for researchers working on the closely related domains of probabilities, trees, algorithms and combinatorics. Basic data structures of Computer Science, such as trees or graphs, can and should be studied from several points of view: as the data structure underlying some algorithms, or as a combinatorial or probabilistic object.

The previous meetings were very well received and established a vivid and increasing cooperation between mathematicians and researchers in computer science. Both communities get their reward from the cooperation. For mathematicians computer science is a rich source of interesting and new structures, which require a systematic approach and provide new insights. For theoretical computer science researcher it is a source of mathematical knowledge and a platform for exchanging problems and for abstract research on theoretical fundamentals. The previous meetings as well as this one showed an ongoing research and an development of new tools and methods, like in probability, combinatorics and singularity analysis. In this sense, the meetings serves as a melting pot for different views, attitudes and cultures.

With the organization of the 2008 Colloquium, we hope to have contributed further progress on topics at the boundary (or closed partly the gap) between probability theory and theoretical computer science. Papers were sought in a wide spectrum of mathematical areas, for instance random trees, stochastic processes, large deviations, branching processes, random walks, discrete probabilities, analytical and enumerative combinatorics, run time analysis of algorithms and data structures, performance evaluation, random generation of combinatorial structures, singularity analysis, logic, number theory, statistics, stochastic geometry and so on. A large Program Committee, guaranteeing wide coverage of subtopics and expertise in a variety of fields, selected 34 papers for a presentation as 30-minute talks and some for a presentation as a poster. Almost all talk presentations appear in this volume of the journal Discrete Mathematics & Theoretical Computer Science. Furthermore, eight one-hour plenary lectures were presented by the following invited speakers (appearing in alphabetical order)

Philippe Chassaing (Université Henri Poincaré, France)
Jean-Francois Le Gall (Université Paris-Sud, France)
Malwina Luczak (The London School of Economics and Political Sience, Great Britain)
Ralph Neininger (Johann Wolfgang Goethe Universität, Germany)
Mathew Penrose (University of Bath, England)
Angelika Steger (ETH Zürich, Switzerland)
Wojciech Szpankowski (Purdue University, USA)
Joseph E. Yukich (Lehigh University, USA).

The papers assembled in this volume offer snapshots of current research. Moreover, some of them, in particular invited talks, include carefully crafted surveys of their field. The variety of topics illustrate the numerous ramifications of the theory of discrete and random discrete structures throughout mathematics and computer science. And they show the interplay of different fields.

I wish to express my gratitude and indebtness to the members of the Program Committee, who I was honoured to chair, to the members of the Organizing Committee, to the invited speakers and to all the authors and participants of the conference contributing to the great success of the conference. Thanks for all the constructive support, fast reports of the referees, sound advice by the organizing committee, help of the editor-in-chief of DMTCS and many more. Especially I like to thank the coorganizers of the meeting, Rudolph Grübel and Ludger Rueschendorf, for sharing the work, Jan Spitzman for his internet support and the edition of this volume, our secretary Mrs. Ceuleman for the autonomous work and Mrs. Riemer at the desk office.

Last but not least, I would like to thank for financial support by the DFG and the Center of Scientific Computing (CSC) in Kiel. Further the Christian-Albrechts-Universität zu Kiel provided substantial help in many respects.

Kiel, September 2008
Uwe Roesler
Chair of the Program Committee

Program Committee

Philippe Chassaing (Université Henri Poincaré, France)
Brigitte Chauvin (Université de Versailles, France)
Michael Drmota (Technische Universität Wien, Austria)
Philippe Flajolet, (INRIA, France)
Danièle Gardy (Université de Versailles, France)
Rudolf Grübel (Leibniz Universität Hannover, Germany)
Uwe Roesler, chair, (Christian-Albrechts-Universität Kiel, Germany)
Ludger Rüschendorf (Albert-Ludwigs-Universität Freiburg, Germany)
Gilles Schaeffer (CNRS, France)
Robert Sedgewick (Princeton University, USA)
Wojciech Szpankowski (Purdue University, USA)
Brigitte Vallée (Université de Caen, France)

The 2007 Conference on Analysis of Algorithms (AofA'07), has been held in Juan-les-Pins near the cities of Antibes and Nice, France, on June 17-22, 2007.

The Analysis of Algorithms is a scientific basis for computation, providing a link between abstract algorithms and the performance characteristics of their implementations in the real world. The general effort to precisely predict the performance of algorithms has come to involve research in analytic combinatorics, the analysis of random discrete structures, asymptotic analysis, exact and limiting distributions, and other fields of inquiry in computer science, probability theory, and enumerative combinatorics.

The Fourth Colloquium on Mathematics and Computer Science is, singularly, the fifth one in a series of events that began at the University of Versailles Saint-Quentin with the ''Colloque Arbres'' in June 1995, then went on to the First and Second Colloquia on Mathematics and Computer Science in September 2000 and 2002, again in Versailles, the fourth edition being hold in Vienna in 2004. These meetings aim at creating a forum for researchers working on the closely related domains of probabilities, trees, algorithms and combinatorics. Basic data structures of Computer Science, such as trees or graphs, can, and should, be studied from several points of view: as the data structure underlying some algorithms, or as a combinatorial or probabilistic object ...

The first meetings in 1995, 2000, 2002 and 2004 were well received both by mathematicians and by computer science researchers, and were followed by a continuously increasing cooperation between both communities. On the one hand, mathematicians found a new source of difficult and interesting questions in the analysis of models for Computer Science. On the other hand, the analysis of algorithms and data structures experienced significant developments with the use of existing tools and methods in probability, statistics and combinatorics, and with the development of new ones. With the organization of the 2006 Colloquium, we hope we made further progress towards establishing a regular meeting place for discussion of topics at the boundary between probabilities, statistics, and fundamental computer science. Papers were sought in a wide spectrum of areas, for instance random trees, stochastic processes, large deviations, branching processes, random walks, discrete probabilities, analytical and enumerative combinatorics, analysis of algorithms and data structures, performance evaluation, random generation of combinatorial structures, and statistics. A large Program Committee, guaranteeing wide coverage of subtopics and expertise in a variety of fields, selected 27 papers for a presentation as 25-minutes talks and 10 other papers were selected for a presentation as posters. All these presentations appear in this volume of proceedings of the journal Discrete Mathematics & Theoretical Computer Science. Furthermore, eight 1-hour invited lectures were presented by Michael Drmota (Vienna), Philippe Flajolet (INRIA), Piotr Indyk (MIT), Grégory Miermont (Orsay), Gilles Schaeffer (École Polytechnique), Laurent Viennot (INRIA), Johan Wästlund (Linköping), Wolfgang Woess (Graz). The invited speakers were free to propose a paper, and that resulted in 4 important contributions to this volume.

Altogether, papers assembled in this volume offer snapshots of current research. At the same time, they illustrate the numerous ramifications of the theory of random discrete structures throughout mathematics and computer science. Many of them, in particular invited lectures, include carefully crafted surveys of their field. I thus hope that this volume may serve both as a reference text and as a smooth introduction to many fascinating aspects of this melting pot of continuous and discrete mathematics.

I wish to express my gratitude and indebtness to the members of the Program Committee who I was honoured to chair, to the members of the Organizing Committee, to the invited speakers and to all the authors and participants of the conference, for each one of them has contributed, in a way or another, to the great success of the conference. I also wish to thank Maxim Krikun for his support, help and advice for the edition of this volume. Jens Gustedt, editor-in-chief of DMTCS, Danièle Gardy, Conrado Martinez, Elahe Zohoorian-Azad and Lucas Gerin were also of a great help.

Last but not least, several public and private institutions provided financial support and other contributions. Special thanks shall be given for the financial and logistic support provided by the Plan Pluriannuel de Formation Informatique, Automatique, Electronique, Electrotechnique Mathématiques (PPF IAEEM), the Centre National de la Recherche Scientifique (CNRS), the Agence Nationale de la Recherche (ANR), the Université Henri Poincaré, the Faculté des Sciences, the Institut Élie Cartan and the city of Nancy.

Nancy, September 2006,
Philippe Chassaing
Chair of the Program Committee

Program Committee Mireille Bousquet-Mélou (Université de Bordeaux 1, France)
Philippe Chassaing, (Université Henri Poincaré, France)
Brigitte Chauvin (Université de Versailles St-Quentin, France)
Luc Devroye (McGill University, Canada)
Michael Drmota (Vienna University of Technology, Austria)
Danièle Gardy (Université de Versailles St-Quentin, France)
Micha Hofri (Worcester Polytechnic Institute, USA)
Hsien-Kuei Hwang (Academia Sinica, Taiwan)
Philippe Jacquet (INRIA, France)
Svante Janson (Uppsala University, Sweden)
Christian Krattenthaler (Universität Wien, Austria)
Nicholas Pippenger (Princeton, USA)
Jim Pitman (Berkeley, USA)
Philippe Robert (INRIA, France)