Olivier Bournez
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Publications

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2024

  1. Manon Blanc and Olivier Bournez. A characterization of polynomial time computable functions from the integers to the reals using discrete ordinary differential equations.
    International Journal of Foundations of Computer Science. To appear. Journal version of \cite{BlancBournezMCU22vantardise}. Preliminary version available on \url{https://arxiv.org/abs/2209.13599}. (BibTeX)
  2. Nathalie Aubrun, Manon Blanc and Olivier Bournez. The domino problem is decidable for robust tilesets.
    CoRR, abs/2402.04438. (BibTeX)
  3. Riccardo Gozzi and Olivier Bournez. Set Descriptive Complexity of Solvable Functions.
    CoRR, abs/2405.19304. (BibTeX)
  4. Olivier Bournez and Riccardo Gozzi. Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations.
    CoRR, abs/2405.00165. (BibTeX)
  5. Olivier Bournez and Riccardo Gozzi. Solving discontinuous initial value problems with unique solutions is equivalent to computing over the transfinite.
    In Symposium on Theoretical Aspects of Computer Science (STACS), Clermont-Ferrand, France.. (BibTeX)
  6. Manon Blanc and Olivier Bournez. Quantifiying the Robustness of Dynamical Systems. Relating Time and Space to Length and Precision.
    In 32nd {EACSL} Annual Conference on Computer Science Logic, {CSL} 2024, February 19-23, 2024, Naples, Italy. Dagstuhl, Germany. (Aniello Murano and Alexandra Silva, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 17:1-17:20. (BibTeX)
  7. Manon Blanc and Olivier Bournez. The complexity of computing in continuous time: space complexity is precision.
    In ICALP: Annual International Colloquium on Automata, Languages and Programming 2024 (ICALP'2024). July. (Karl Bringmann, Martin Grohe, Gabriele Puppis, and Ola Svensson, Eds.) LIPICS. (BibTeX)
  8. Olivier Bournez, Florent Becker, Jean-Loup Carr\'e, Mathieu Liedloff and G\'erard Rozsavolgyi. Informatique tout-en-un MP2I-MPI.
    Dunod. {\`a} para{\^\i}tre. (BibTeX)

2023

  1. Olivier Bournez, Riccardo Gozzi, Daniel Silva Gra\cca and Amaury Pouly. A continuous characterization of PSPACE using polynomial ordinary differential equations.
    Journal of Complexity, 77:101755Elsevier. (BibTeX)
  2. Manon Blanc and Olivier Bournez. Measuring robustness of dynamical systems. Relating time and space to length and precision.
    Technical report. (BibTeX)
  3. Olivier Bournez and Arnaud Durand. A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations.
    Computational Complexity, 32(2):7Springer. (BibTeX)
  4. Olivier Bournez, Johanne Cohen and Valentin Dardilhac. On the $\delta$-decidability of decision problems for neural network questions.
    In Computability, Continuity, Constructivity - from Logic to Algorithms CCC'23.. (BibTeX)
  5. Manon Blanc and Olivier Bournez. Characterisations of polynomial-time and -space complexity classes over the reals Characterisations of polynomial-time and -space complexity classes over the reals.
    In Continuity, Computability, Constructivity. From Logic to Algorithms. CCC'23. Kyoto, Japan, September. (BibTeX)
  6. Olivier Bournez and Riccardo Gozzi. Discontinuous IVPs with unique solutions.
    In Continuity, Computability, Constructivity. From Logic to Algorithms. CCC'23. Kyoto, Japan, September. (BibTeX)
  7. Olivier Bournez, Johanne Cohen and Valentin Dardilhac. On the $\delta$-decidability of decision problems for neural network questions.
    In Twentieth International Conference on Computability and Complexity in Analysis CCA'23. Dubronik, Croatia, September. (BibTeX)
  8. Olivier Bournez and Riccardo Gozzi. Discontinuous IVPs with unique solutions.
    In Twentieth International Conference on Computability and Complexity in Analysis CCA'23. Dubronik, Croatia, September. (BibTeX)
  9. Manon Blanc and Olivier Bournez. Characterisations of polynomial-time and -space complexity classes over the reals Characterisations of polynomial-time and -space complexity classes over the reals.
    In Twentieth International Conference on Computability and Complexity in Analysis CCA'23. Dubronik, Croatia, September. (BibTeX)
  10. Manon Blanc and Olivier Bournez. Measuring the robustness of the dynamical systems. Relating time and space to length and precision.
    In 7th International Workshop "Women in Logic" Wil'2023. Rome, Italy, July. (BibTeX)
  11. Reachability Problems - 17th International Conference, RP 2023, Nice, France, October 11-13, 2023, Proceedings.
    (Olivier Bournez, Enrico Formenti and Igor Potapov, Eds.)volume 14235 of Lecture Notes in Computer Science, Springer. (BibTeX)
  12. Manon Blanc and Olivier Bournez. A Characterisation of Functions Computable in Polynomial Time and Space over the Reals with Discrete Ordinary Differential Equations: Simulation of Turing Machines with Analytic Discrete ODEs.
    In 48th International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2023, August 28 to September 1, 2023, Bordeaux, France. (J\'er\^ome Leroux, Sylvain Lombardy and David Peleg, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 21:1-21:15, . Schloss Dagstuhl-Leibniz-Zentrum f{\"u}r Informatik. (BibTeX)
  13. Manon Blanc and Olivier Bournez. Simulation of Turing machines with analytic discrete ODEs: FPTIME and FPSPACE over the reals characterised with discrete ordinary differential equations.
    CoRR, abs/2307.11747. (BibTeX)

2022

  1. Olivier Bournez and Quentin Guilmant. Surreal fields stable under exponential and logarithmic functions.
    . Submitted. (BibTeX)
  2. Olivier Bournez. Programming with Ordinary Differential Equations: Some First Steps Towards a Programming Language.
    In Revolutions and Revelations in Computability - 18th Conference on Computability in Europe, CiE 2022, Swansea, UK, July 11-15, 2022, Proceedings. (Ulrich Berger, Johanna N. Y. Franklin, Florin Manea and Arno Pauly, Eds.) Springer, pages 39-51. (BibTeX)
  3. Manon Blanc and Olivier Bournez. A Characterization of Polynomial Time Computable Functions from the Integers to the Reals Using Discrete Ordinary Differential Equations.
    In Machines, Computations, and Universality - 9th International Conference, {MCU} 2022, Debrecen, Hungary, August 31 - September 2, 2022, Proceedings. (J\'er\^ome Durand-Lose and Gy\"orgy Vaszil, Eds.) Springer, pages 58-74. {MCU'22 Best Student Paper Award}. (BibTeX)

2021

  1. Olivier Bournez and Amaury Pouly. A Survey on Analog Models of Computation.
    In Handbook of Computability and Complexity in Analysis (Brattka, Vasco and Hertling, Peter, Eds.). Springer. (BibTeX)

2020

  1. Olivier Bournez and Amaury Pouly. A Universal Ordinary Differential Equation.
    Logical Methods in Computer Science, 16(1). (BibTeX)
  2. Olivier Bournez. Computability, Complexity and Programming with Ordinary Differential Equations (Invited Talk).
    In 37th International Symposium on Theoretical Aspects of Computer Science, {STACS} 2020, March 10-13, 2020, Montpellier, France. (Christophe Paul and Markus Bl\"aser, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 3:1-3:13, . Schloss Dagstuhl-Leibniz-Zentrum f{\"u}r Informatik. (BibTeX)

2019

  1. Olivier Bournez and Sabrina Ouazzani. Continuous Ordinary Differential Equations and Transfinite Computations.
    ArXiv e-prints. (BibTeX)
  2. Olivier Bournez. La revanche du calcul analogique.
    Blog 'Binaire' du journal 'Le Monde'. (BibTeX)
  3. Olivier Bournez and Arnaud Durand. Recursion Schemes, Discrete Differential Equations and Characterization of Polynomial Time Computations.
    In 44th International Symposium on Mathematical Foundations of Computer Science, {MFCS} 2019, August 26-30, 2019, Aachen, Germany. (Peter Rossmanith, Pinar Heggernes and Joost-Pieter Katoen, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 23:1-23:14. (BibTeX)

2018

  1. Hugo Bazille, Olivier Bournez, Walid Gomaa and Amaury Pouly. On the complexity of bounded time and precision reachability for piecewise affine systems.
    Theoretical Computer Science, 735:132-146. (BibTeX)
  2. Olivier Bournez, Johanne Cohen and Mika\"el Rabie. Homonym Population Protocols.
    Theory of Computing Systems, 62(5):1318-1346. (BibTeX)
  3. Olivier Bournez, Oleksiy Kurganskyy and Igor Potapov. Reachability Problems for One-Dimensional Piecewise Affine Maps.
    Int. J. Found. Comput. Sci., 29(4):529-549. (BibTeX)
  4. Olivier Bournez and Amaury Pouly. A Survey on Analog Models of Computation.
    Technical report. (BibTeX)
  5. Olivier Bournez and Sabrina Ouazzani. Cheap Non-standard Analysis and Computability.
    Technical report. \url{http://arxiv.org/abs/1804.09746}. (BibTeX)
  6. Olivier Bournez and Sabrina Ouazzani. Cheap Non-Standard Analysis and Computability: Some Applications.
    In 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, {SYNASC} 2018, Timisoara, Romania, September 20-23, 2018.. {IEEE}, pages 149-156. (BibTeX)
  7. Olivier Bournez, Arnaud Durand and Sabrina Ouazzani. Recursion schemes, discrete differential equations and characterization of polynomial time computation.
    CoRR, abs/1810.02241. (BibTeX)
  8. Olivier Bournez. Ordinary Differential Equations \& Computability.
    In 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, {SYNASC} 2018, Timisoara, Romania, September 20-23, 2018.. {IEEE}, pages 3-5. (BibTeX)

2017

  1. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. On the functions generated by the general purpose analog computer.
    Information and Computation, 257:34-57. (BibTeX)
  2. Olivier Bournez and Amaury Pouly. A Universal Ordinary Differential Equation.
    In 44th International Colloquium on Automata, Languages, and Programming, {ICALP} 2017, July 10-14, 2017, Warsaw, Poland. (Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn and Anca Muscholl, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 116:1-116:14. (BibTeX)
  3. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length.
    Journal of the ACM, 64(6):38:1-38:76. (BibTeX)
  4. Fran\ccois Fages, Guillaume Le Guludec, Olivier Bournez and Amaury Pouly. Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs.
    In Computational Methods in Systems Biology - 15th International Conference, {CMSB} 2017, Darmstadt, Germany, September 27-29, 2017, Proceedings. (J\'er\^ome Feret and Heinz Koeppl, Eds.) Springer, pages 108-127. (BibTeX)

2016

  1. Olivier Bournez, Nachum Dershowitz and Pierre N\'eron. Axiomatizing Analog Algorithms.
    In Pursuit of the Universal - 12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016, Proceedings. (Arnold Beckmann, Laurent Bienvenu and Natasa Jonoska, Eds.) Springer, pages 215-224. (BibTeX)
  2. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. Computing with polynomial ordinary differential equations.
    Journal of Complexity, 36:106-140. (BibTeX)
  3. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length.
    CoRR, abs/1601.05360. (BibTeX)
  4. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length: The General Purpose Analog Computer and Computable Analysis Are Two Efficiently Equivalent Models of Computations.
    In 43rd International Colloquium on Automata, Languages, and Programming, {ICALP} 2016, July 11-15, 2016, Rome, Italy. (Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani and Davide Sangiorgi, Eds.) Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik, pages 109:1-109:15. (BibTeX)

2015

  1. Olivier Bournez, Johanne Cohen and Mika\"el Rabie. Homonym Population Protocols.
    In Networked Systems - Third International Conference, {NETYS} 2015, Agadir, Morocco, May 13-15, 2015, Revised Selected Papers. (Ahmed Bouajjani and Hugues Fauconnier, Eds.) Springer, pages 125-139. (BibTeX)
  2. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. Rigorous Numerical Computation of Polynomial Differential Equations Over Unbounded Domains.
    In Mathematical Aspects of Computer and Information Sciences - 6th International Conference, {MACIS} 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers. (Ilias S. Kotsireas, Siegfried M. Rump and Chee K. Yap, Eds.) Springer, pages 469-473. (BibTeX)

2014

  1. Bournez, Olivier. Fondements de l'Informatique: Logique, Mod\`eles, Calculs.
    Ecole Polytechnique. 234 pages. (BibTeX)
  2. Bournez, Olivier, Dowek, Gilles, Gilleron, R\'emi, Grigorieff, Serge, Marion, Jean-Yves, Perdrix, Simon and Tison, Sophie. Informatique th\'eorique : calculabilit\'e, d\'ecidabilit\'e et logique.
    In {L'I.A. fronti{\`e}res et Applications}. (Marquis, Pierre, Papini, Odile and Prades, Henri, Eds.). http://www.cepadues.com/, C{\'e}padu{\`e}s Editions. (BibTeX)
  3. Bournez, Olivier, Dowek, Gilles, Gilleron, R\'emi, Grigorieff, Serge, Marion, Jean-Yves, Perdrix, Simon and Tison, Sophie. Informatique th\'eorique : complexit\'e, automates et au-del\`a.
    In {L'I.A. fronti{\`e}res et Applications}. (Marquis, Pierre, Papini, Odile and Prades, Henri, Eds.). http://www.cepadues.com/, C{\'e}padu{\`e}s Editions. (BibTeX)
  4. Hugo Bazille, Olivier Bournez, Walid Gomaa and Amaury Pouly. On The Complexity of Bounded Time Reachability for Piecewise Affine Systems.
    In Reachability Problems - 8th International Workshop, {RP} 2014, Oxford, UK, September 22-24, 2014. Proceedings. (Jo\"el Ouaknine, Igor Potapov and James Worrell, Eds.) Springer, pages 20-31. (BibTeX)

2013

  1. Bournez, Olivier, Chalopin, J\'er\'emie, Cohen, Johanne, Koegler, Xavier and Mika\"el, Rabie. Population Protocols that Correspond to Symmetric Games.
    International Journal of Unconventional Computation, 9(1--2):5-36. (BibTeX)
  2. Bournez, Olivier and Cohen, Johanne. Learning Equilibria in Games by Stochastic Distributed Algorithms.
    In Computer and Information Sciences III (Gelenbe, Erol and Lent, Ricardo, Eds.), pages 31-38. Springer London. (BibTeX)
  3. Bournez, Olivier, Gra\cca, Daniel S. and Pouly, Amaury. Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer.
    In Theory and Applications of Models of Computation, 10th International Conference, TAMC 2013, Hong Kong, China, May 20-22, 2013. Proceedings (TAMC'2013). (Chan, T.-H. Hubert, Lau, Lap Chi and Trevisan, Luca, Eds.) Springer, pages 169-180. (BibTeX)
  4. Bournez, Olivier, Gra\cca, Daniel S. and Hainry, Emmanuel. Computation with perturbed dynamical systems.
    Journal of Computer System Science, 79(5):714-724. (BibTeX)
  5. Bournez, Olivier and Lef\`evre, Jonas. Population Protocols on Graphs: A Hierarchy.
    In Spatial Computing Workship (SCW'2013). (Mauri, Giancarlo, Dennunzio, Alberto, Manzoni, Luca and Porreca, Antonio E., Eds.) Springer. (BibTeX)
  6. Olivier Bournez, Daniel Silva Gra\cca, Amaury Pouly and Ning Zhong. Computability and computational complexity of the evolution of nonlinear dynamical systems.
    In The Nature of Computation. Logic, Algorithms, Applications - 9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013. Proceedings. (Paola Bonizzoni, Vasco Brattka and Benedikt L\"owe, Eds.) Springer, pages 12-21. (BibTeX)
  7. Olivier Bournez, Jonas Lef\`evre and Mika\"el Rabie. Trustful Population Protocols.
    In Distributed Computing - 27th International Symposium, {DISC} 2013, Jerusalem, Israel, October 14-18, 2013. Proceedings. (Yehuda Afek, Eds.) Springer, pages 447-461. (BibTeX)

2012

  1. Bournez, Olivier, Dershowitz, Nachum and Falkovich, Evgenia. Towards an Axiomatization of Simple Analog Algorithms.
    In Theory and Applications of Models of Computation - 9th Annual Conference, TAMC 2012, Beijing, China, May 16-21, 2012. Proceedings. (Agrawal, Manindra, Cooper, S. Barry and Li, Angsheng, Eds.) Spinger-Verlag, pages 525-536. (BibTeX)
  2. Olivier Bournez, Pierre Fraigniaud and Xavier Koegler. Computing with Large Populations Using Interactions.
    In Mathematical Foundations of Computer Science 2012 - 37th International Symposium, {MFCS} 2012, Bratislava, Slovakia, August 27-31, 2012. Proceedings. (Branislav Rovan, Vladimiro Sassone and Peter Widmayer, Eds.) Springer, pages 234-246. (BibTeX)
  3. Bournez, Olivier and Dowek, Gilles. Physics and Computation Special Issue.
    Natural Computing, 11(1):1. (BibTeX)
  4. Olivier Bournez, Daniel Silva Gra\cca and Amaury Pouly. On the complexity of solving initial value problems.
    In International Symposium on Symbolic and Algebraic Computation, ISSAC'12, Grenoble, France - July 22 - 25, 2012. (Joris van der Hoeven and Mark van Hoeij, Eds.) {ACM}, pages 115-121. (BibTeX)

2011

  1. Guillaume Aupy and Olivier Bournez. On the number of binary-minded individuals required to compute sqrt(1/2).
    Theoretical Computer Science, 412(22):2262-2267. (BibTeX)
  2. Olivier Bournez, Pierre Fraigniaud, Xavier Koegler. Computing with Large Populations.
    Technical report. Technical Report. (BibTeX)
  3. Bournez, Olivier and Potapov, Igor. Reachability Problems (RP 2009) Special Issue.
    volume 22 of International Journal of Foundations of Computer Science. (BibTeX)
  4. Olivier Bournez, Daniel Gra\~A\Sa, Amaury Pouly. Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains.
    In Mathematical Foundations of Computer Science, MFCS'11., pages 170-181. (BibTeX)
  5. Bournez, Olivier, Gomaa, Walid and Hainry, Emmanuel. Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions.
    IJUC, 7(5):331-351. (BibTeX)
  6. Bournez, Olivier, Chalopin, J\'er\'emie, Cohen, Johanne, Koegler, Xavier and Rabie, Mika\"el. Computing with Pavlovian Populations.
    In Principles of Distributed Systems - 15th International Conference, OPODIS 2011, Toulouse, France, December 13-16, 2011. Proceedings.. Springer, pages 409-420. (BibTeX)
  7. Bournez, Olivier. Fondements de l'Informatique: Logique, Mod\`eles, Calculs.
    Ecole Polytechnique. (BibTeX)

2010

  1. Bournez, Olivier, Gra\cca, Daniel S. and Hainry, Emmanuel. Robust Computations with Dynamical Systems.
    In Mathematical Foundations of Computer Science, MFCS'2010.. Springer, pages 198-208. (BibTeX)
  2. Bournez, Olivier. Algorithmes et Complexit\'e.
    Ecole Polytechnique. 199 pages. (BibTeX)

2009

  1. Bournez, Olivier, Chassaing, Philippe, Cohen, Johanne, Gerin, Lucas and Koegler, Xavier. On the Convergence of Population Protocols When Population Goes to Infinity.
    Applied Mathematics and Computation, 215(4):1340-1350. (BibTeX)
  2. Barth, Dominique, Bournez, Olivier, Boussaton, Octave and Cohen, Johanne. Distributed Learning of Equilibria in a Routing Game.
    Parallel Processing Letters, 19:189-204. (BibTeX)
  3. Bournez, Olivier, Gomaa, Walid and Hainry, Emmanuel. Characterizing algebraically computable and polynomial time functions over the reals.
    In Submitted... Submitted. (BibTeX)
  4. Bournez, Olivier and Cohen, Johanne. Learning Equilibria in Games by Stochastic Distributed Algorithms..
    Technical report. Submitted. (BibTeX)
  5. Bournez, Olivier and Cohen, Johanne. Stochastic Learning of Equilibria in Games: The Ordinary Differential Equation Method..
    Technical report. http://www.lix.polytechnique.fr/$\tilde{\ }$bournez/uploads/Main/Papier-BC09sod.pdf. (BibTeX)
  6. Bournez, Olivier and Cohen, Johanne. Pure Nash Equilibria Can be Learned Efficiently in Potential Games By a Wide Class of Fully Distributed Algorithm..
    Technical report. http://www.lix.polytechnique.fr/$\tilde{\ }$bournez/uploads/Main/Papier-BC09sod.pdf. (BibTeX)
  7. Bournez, Olivier. Th\`ese de Church. Autres Mod\`eles de Calculs.
    Technical report. (BibTeX)
  8. Olivier Bournez, Walid Gomaa and Hainry, Emmanuel. Implicit complexity in recursive analysis.
    In Logic and Computational Complexity.. (BibTeX)
  9. Dominique Barth, Olivier Bournez, Octave Boussaton and Johanne Cohen. A dynamic approach for load balancing.
    In 4th International Conference on Performance Evaluation Methodologies and Tools, {VALUETOOLS} '09, Pisa, Italy, October 20-22, 2009. Pisa, Italy, October. (Giovanni Stea, Jean Mairesse and Jos\'e Mendes, Eds.) {ICST/ACM}, page 60. (BibTeX)
  10. Bournez, Olivier and Potapov, Igor. Reachability Problems, 3rd International Workshop, RP 2009, Palaiseau, France, September 23-25, 2009. Proceedings.
    (Bournez, Olivier and Potapov, Igor, Eds.)volume 5797 of Lecture Notes in Computer Science, Springer. (BibTeX)

2008

  1. Olivier Bournez and Manuel L. Campagnolo. A Survey on Continuous Time Computations.
    In New Computational Paradigms. Changing Conceptions of What is Computable. (Cooper, S.B., L\"owe, B. and Sorbi, A., Eds.). New York, Springer-Verlag, pages 383-423. (BibTeX)
  2. Barth, Dominique, Bournez, Olivier, Boussaton, Octave and Cohen, Johanne. A Dynamical Approach for Load Balancing.
    Technical report, LORIA/INRIA. Submitted. Available on {\tt http://www.lix.polytechnique.fr/\~{}bournez/load/Soumis-Octave-Fev-2008.pdf}. (BibTeX)
  3. Bournez, Olivier and Garnier, Florent. Termination in finite mean time of a CSMA/CA Termination in finite mean time of a CSMA/CA rule-based model.
    Technical report, LORIA/INRIA. Submitted. (BibTeX)
  4. Bournez, Olivier and Garnier, Florent. Termination in finite mean time of a CSMA/CA Termination in finite mean time of a CSMA/CA rule-based model.
    Technical report, LORIA/INRIA. Submitted. (BibTeX)
  5. Bournez, Olivier, Chassaing, Philippe, Cohen, Johanne, Gerin, Lucas and Koegler, Xavier. On the Convergence of a Population Protocol When Population Goes to Infinity.
    In Physics and Computations, Worshop of Unconventional Computation 2008, UC 2008. Vienna, Austria, August 25-28. (BibTeX)
  6. Barth, Dominique, Bournez, Olivier, Boussaton, Octave and Cohen, Johanne. Distributed Learning of Wardrop Equilibria.
    In Unconventional Computation 2008, UC 2008. Vienna, Austria, August 25-28. Springer, pages 19-32. (BibTeX)
  7. Olivier Bournez, J\'er\'emie Chalopin, Johanne Cohen and Xavier Koegler. Playing With Population Protocols.
    In Proceedings International Workshop on The Complexity of Simple Programs, {CSP} 2008, Cork, Ireland, 6-7th December 2008. Cork, Irland, December 6-7th. (Turlough Neary, Damien Woods, Anthony Karel Seda and Niall Murphy, Eds.) Pages 3-15. (BibTeX)

2007

  1. Barth, D., Bournez, O., Boussaton, O. and Cohen, J.. Convergences et dynamiques du routage dans les r\'eseaux.
    In Journ{\'e}es P{\^o}le ResCom. September. (BibTeX)
  2. Bournez, Olivier and Hainry, Emmanuel. On the Computational Capabilities of Several Models.
    In Machines, Computations and Universality (MCU'2007). September 10-13. Springer. (BibTeX)
  3. Bournez, Olivier, Campagnolo, Manuel L., Gra\c ca, Daniel S. and Hainry, Emmanuel. Polynomial differential equations compute all real computable functions on computable compact intervals.
    Journal of Complexity, 23(3):317-335. (BibTeX)
  4. Bournez, Olivier, Campagnolo, Manuel L., Gra\cca, Daniel and S. Hainry, Emmanuel. Polynomial differential equations compute all real computable functions on computable compact intervals.
    Journal of Complexity, 23(3):317-335. (BibTeX)

2006

  1. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  2. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  3. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  4. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  5. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  6. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  7. Bournez, Olivier. Mod\`eles Continus. Calculs. Algorithmique Distribu\'ee.
    PhD thesis. (BibTeX)
  8. Bournez, Olivier, Campagnolo, Manuel L., Gra\c ca, Daniel S. and Hainry, Emmanuel. The General Purpose Analog Computer and Computable Analysis are Two Equivalent Paradigms of Analog Computation.
    In Theory and Applications of Models of Computation, Third International Conference, {TAMC} 2006, Beijing, China, May 15-20, 2006, Proceedings. (Cai, Jin-yi, Cooper, S. Barry and Li, Angsheng, Eds.) Springer, pages 631-643. (BibTeX)
  9. Bournez, Olivier and Garnier, Florent. Proving Positive Almost Sure Termination Under Strategies.
    In 17th International Conference on Rewriting Techniques and Applications (RTA'2006). Seattle, WA, USA. (Pfenning, Frank, Eds.) Springer, pages 357-371. (BibTeX)
  10. Bournez, Olivier. How much can analog and hybrid systems be proved (super-)Turing.
    Applied Mathematics and Computation, 178(1):58-71. (BibTeX)
  11. Bournez, Olivier and Hainry, Emmanuel. Recursive Analysis Characterized as a Class of Real Recursive Functions.
    Fundamenta Informaticae, 74(4):409-433. (BibTeX)
  12. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Implicit Complexity over an Arbitrary Structure: Quantifier Alternations.
    Information and Computation, 202(2):210-230. (BibTeX)
  13. Sylvie Dela\"et, Dominique Barth, Olivier Bournez Johanne Cohen Loubna Echabbi. Existence of a Nash Equilibria in a pricing game adapted to BGP.
    Technical report, LRI. (BibTeX)

2005

  1. Olivier Bournez, Liliana Ibanescu and H\'el\`ene Kirchner. From Chemical Rules to Term Rewriting.
    In Proceedings of the 6th International Workshop on Rule-Based Programming, RULE@RDP 2005, Nara, Japan, April 23, 2005. Nara, Japan, April. (Horatiu Cirstea and Narciso Mart\'\i-Oliet, Eds.) Elsevier, pages 113-134. (BibTeX)
  2. Olivier Bournez and Florent Garnier. Proving Positive Almost-Sure Termination.
    In Term Rewriting and Applications, 16th International Conference, {RTA} 2005, Nara, Japan, April 19-21, 2005, Proceedings. Nara, Japan. (J\"urgen Giesl, Eds.) Springer, pages 323-337. (BibTeX)
  3. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time.
    Journal of Logic and Computation, 15(1):41-58. (BibTeX)
  4. Bournez, Olivier and Hainry, Emmanuel. Elementarily Computable Functions Over the Real Numbers and $\mathbbR$-Sub-Recursive Functions.
    Theoretical Computer Science, 348(2--3):130-147. (BibTeX)
  5. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Logical Characterizations of $P_\mathcalK$ and $NP_\mathcalK$ Over an Arbitrary Structure $K$.
    In 3rd APPSEM II Workshop (APPSEM'05), Frauenchiemsee, Germany, 2005. Also accepted for presentation at \textit{CIE 2005: New Computational Paradigms.}.. (BibTeX)
  6. Bournez, Olivier, Soussan, Terence and Tavernier, Bertrand. Symbolic Simulation and Formal Verification of Updatable Timed Automata.
    Technical report, LORIA. (BibTeX)
  7. Bournez, Olivier, Garnier, Florent and Kirchner, Claude. Termination in finite mean time of a CSMA/CA rule-based model.
    Technical report, LORIA, Nancy. (BibTeX)

2004

  1. Bournez, Olivier, Soussan, T\'erence and Tavernier, Bertrand. Symbolic Simulation and Formal Verification of Updatable Timed Automata using a Rewrite System.
    Technical report, LORIA. (BibTeX)
  2. Olivier Bournez, Felipe Cucker, Paulin Jacob\'e de Naurois and Jean-Yves Marion. Tailoring Recursion to Characterize Non-Deterministic Complexity Classes over Arbitrary Structures.
    In Exploring New Frontiers of Theoretical Informatics, {IFIP} 18th World Computer Congress, {TC1} 3rd International Conference on Theoretical Computer Science (TCS2004), 22-27 August 2004, Toulouse, France. Toulouse, France, august. (Jean-Jacques L\'evy, Ernst W. Mayr and John C. Mitchell, Eds.) Kluwer/Springer, pages 409-422. (BibTeX)
  3. Bournez, Olivier and Hainry, Emmanuel. Real Recursive Functions and Real Extentions of Recursive Functions.
    In Machines, Computations and Universality (MCU'2004). Saint-Petersburg, Russia, September. (Margenstern, Maurice, Eds.). (BibTeX)
  4. Bournez, Olivier and Hainry, Emmanuel. An Analog Characterization of Elementarily Computable Functions Over the Real Numbers.
    In 31th International Colloquium on Automata Languages and Programming (ICALP'04). Turku, Finland. Springer, pages 269-280. (BibTeX)
  5. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Tailoring Recursion to Characterize Non-Deterministic Complexity Classes Over Arbitrary Structures.
    In In 2nd APPSEM II Workshop (APPSEM'04). April. (BibTeX)
  6. Bournez, Olivier and Hainry, Emmanuel. An Analog Characterization of Elementarily Computable Functions Over the Real Numbers.
    In In 2nd APPSEM II Workshop (APPSEM'04). Tallinn, Estonia, April. (BibTeX)

2003

  1. Bournez, Olivier. Fuzzy Equational Theories.
    Technical report, LORIA. (BibTeX)
  2. Bournez, Olivier, Hoyrup, Mathieu and Kirchner, Claude. Logique de r\'e\'ecriture probabiliste.
    Technical report, LORIA. (BibTeX)
  3. Bournez, Olivier and Hoyrup, Mathieu. Rewriting Logic and Probabilities.
    In Rewriting Techniques and Applications, 14th International Conference, RTA 2003, Valencia, Spain, June 9-11, 2003, Proceedings. June. (Nieuwenhuis, Robert, Eds.) Springer, pages 61-75. (BibTeX)
  4. Bournez, Olivier, C\^ome, Guy-Marie, Conraud, Val\'erie, Kirchner, H\'el\`ene and Ibanescu, Liliana. A Rule-Based Approach for Automated Generation of Kinetic Chemical Mechanisms..
    In Rewriting Techniques and Applications, 14th International Conference, RTA 2003, Valencia, Spain, June 9-11, 2003, Proceedings. June. (Nieuwenhuis, Robert, Eds.) Springer, pages 30-45. (BibTeX)
  5. Bournez, Olivier, Habib, Mohamed El, Kirchner, Claude, Kirchner, H\'el\`ene, Marion, Jean-Yves and Merz, Stephan. The QSL Plateform at LORIA.
    In First QPQ Workshop on Deductive Software Components. Miami, Florida, July 28, pages 9-12. CADE-19 Workshop, {ftp://ftp.csl.sri.com/pub/users/shankar/QPQ03.pdf}. (BibTeX)
  6. Bournez, Olivier, C\^ome, Guy-Marie, Conraud, Val\'erie, Kirchner, H\'el\`ene and Ibanescu, Liliana. Automated Generation of Kinetic Chemical Mechanisms Using Rewriting.
    In International Conference on Computational Science - ICCS 2003, Melbourne, June 2-4, 2003, Proceedings, Part III. (Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y. and Gorbachev, Y.E., Eds.) Springer, pages 367-376. (BibTeX)
  7. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Safe Recursion Over an Arbitrary Structure: PAR, PH and PH.
    In Fifth International Worshop on Implicit Computational Complexity - ICC'2003. Ottawa, Canada. (Dawar, Anuj, Eds.). (BibTeX)
  8. Bournez, Olivier, Cucker, Felipe, de Naurois, Paulin Jacob\'e and Marion, Jean-Yves. Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time..
    In Foundations of Software Science and Computational Structures, 6th International Conference (FOSSACS'2003). Warsaw. (Gordon, Andrew D., Eds.) Springer, pages 185-199. (BibTeX)
  9. Bournez, Olivier. Fuzzy Equational Theories.
    Technical report, LORIA. (BibTeX)

2002

  1. Bournez, Olivier and Kirchner, Claude. Probabilistic rewrite strategies: Applications to ELAN.
    In Rewriting Techniques and Applications. jul22-24. (Tison, Sophie, Eds.) Springer-Verlag, pages 252-266. (BibTeX)
  2. Bournez, Olivier. A Generalization of Equational Proof Theory?.
    In Process Algebra and Probabilistic Methods : Performance Modeling and Verification, 2nd Joint International Workshop. jul25--26. (Hermanns, Holger and Segala, Roberto, Eds.) Springer-Verlag, pages 208-209. (BibTeX)
  3. Bournez, Olivier and Branicky, Michael. The Mortality Problem for Matrices of Low Dimensions.
    Theory of Computing Systems, 35(4):433-448. (BibTeX)
  4. Bournez, Olivier, de Naurois, Paulin and Marion, Jean-Yves. Safe recursion and calculus over an arbitrary structure.
    In Implicit Computational Complexity - ICC'02. Copenhagen, Denmark, July. (BibTeX)

2001

  1. Beffara, Emmanuel, Bournez, Olivier, Kacem, Hassen and Kirchner, Claude. Verification of timed automata using rewrite rules and strategies.
    In Sixth Annual Workshop of the ERCIM Working Group on Constraints. Prague, jun18--20,. (BibTeX)
  2. Blondel, Vincent, Bournez, Olivier, Koiran, Pascal, Papadimitriou, Christos and Tsitsiklis, John. Deciding Stability and Mortality of Piecewise Affine Dynamical Systems.
    Theoretical Computer Science A, 1--2(255):687-696. (BibTeX)
  3. Blondel, Vincent D., Bournez, Olivier, Koiran, Pascal and Tsitsiklis, John. The stability of saturated linear dynamical systems is undecidable.
    Journal of Computer and System Science, 62(3):442-462. (BibTeX)
  4. Beffara, Emmanuel, Bournez, Olivier, Kacem, Hassen and Kirchner, Claude. Verification of timed automata using rewrite rules and strategies.
    In Proceedings BISFAI 2001, Seventh Biennial Bar-Ilan International Symposium on the Foundations of Artificial Intelligence. Ramat-Gan, Israel, jun25--27,. (Dershowitz, Nachum and Frank, Ariel, Eds.). (BibTeX)

2000

  1. Bournez, Olivier and Maler, Oded. On the representation of timed polyhedra.
    In International Colloquium on Automata Languages and Programming (ICALP'00). Geneva, Switzerland, 9--15~jul. Springer, pages 793-807. (BibTeX)
  2. Blondel, Vincent D., Bournez, Olivier, Koiran, Pascal and Tsitsiklis, John N.. The stability of saturated linear dynamical systems is undecidable.
    In {Symposium on Theoretical Aspects of Computer Science (STACS), Lille, France}. feb. (Tison, Horst Reichel Sophie, Eds.) Springer-Verlag, pages 479-490. (BibTeX)
  3. Asarin, Eugene, Bournez, Olivier, Dang, Thao, Maler, Oded and Pnueli, Amir. Effective Synthesis of Switching Controllers for Linear Systems.
    Proceedings of the IEEE, Special Issue on `Hybrid Systems'', 88(7):1011-1025. (BibTeX)
  4. Asarin, Eugene, Bournez, Olivier, Dang, Thao and Maler, Oded. Approximate reachability analysis of piecewise-linear dynamical systems.
    In {Hybrid Systems\,: Computation and Control (HSCC'00), Pittsburgh (USA)}. March 23-25 2000. Springer-Verlag, pages 20-31. (BibTeX)

1999

  1. Bournez, Olivier. Complexit\'e Algorithmique des Syst\`emes Dynamiques Continus et Hybrides.
    PhD thesis. (BibTeX)
  2. Bournez, Olivier. Achilles and the Tortoise climbing up the hyper-arithmetical hierarchy.
    Theoretical Computer Science, 210(1):21-71. (BibTeX)
  3. Bournez, Olivier. Some bounds on the computational power of Piecewise Constant Derivative systems.
    Theory of Computing Systems, 32(1):35-67. (BibTeX)
  4. Bournez, Olivier, Maler, Oded and Pnueli, Amir. Orthogonal polyhedra: Representation and Computation.
    In Hybrid Systems: Computation and Control - HSCC'99. Nijmegen, Pays-Bas, 29--31mar, pages 46-60. (BibTeX)

1998

  1. Gros, Patrick, Bournez, Olivier and Boyer, Edmond. Using Local Planar Geometric invariants to Match and Model Images of Line Segments.
    Computer Vision and Image Understanding: CVIU, 69(2):135-155. (BibTeX)
  2. Bournez, Olivier and Branicky, Michael B.. On matrix mortality in low dimensions.
    In Open Problems in Mathematical Systems and Control Theory. (Blondel, V. D., Sontag, E. D., Vidyasagar, M. and Willems, J. C., Eds.), Springer-Verlag, London, pages 67-70. (BibTeX)

1997

  1. Olivier Bournez. Some Bounds on the Computational Power of Piecewise Constant Derivative Systems (Extended Abstract).
    In Automata, Languages and Programming, 24th International Colloquium, ICALP'97, Bologna, Italy, 7-11 July 1997, Proceedings. Bologne, Italie, 7--11~jul. (Pierpaolo Degano, Roberto Gorrieri and Alberto Marchetti-Spaccamela, Eds.) Springer, pages 143-153. (BibTeX)

1996 and before

  1. Bournez, Olivier and Cosnard, Michel. On the computational power of dynamical systems and hybrid systems.
    Theoretical Computer Science, 168(2):417-459. (BibTeX)
  2. Joseph L. Mundy, Rupert W. Curwen, Jane Liu, Charlie Rothwell, Andrew Zisserman and David A. Forsyth. MORSE: An Architecture for 3D Object Recognition Based on Invariants.
    In Recent Developments in Computer Vision, Second Asian Conference on Computer Vision, {ACCV} '95, Singapore, December 5-8, 1995, Invited Session Papers. Monterey (CA), USA, 13--16nov. (Stan Z. Li, Dinesh P. Mital, Eam Khwang Teoh and Han Wang, Eds.) Springer, pages 425-434. (BibTeX)