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 Olivier Bournez

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Average citations per article6.66
Citation Count293
Publication count44
Publication years1996-2017
Available for download3
Average downloads per article79.33
Downloads (cumulative)238
Downloads (12 Months)103
Downloads (6 Weeks)26
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44 results found Export Results: bibtexendnoteacmrefcsv

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1 published by ACM
October 2017 Journal of the ACM (JACM): Volume 64 Issue 6, November 2017
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 26,   Downloads (12 Months): 89,   Downloads (Overall): 89

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The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class P of languages computable in polynomial time in terms of differential equations with polynomial right-hand side. This result gives a purely continuous ...
Keywords: computable analysis, continuous-time models of computation, Analog models of computation, computational complexity, ordinary differential equations, implicit complexity

2
October 2016 Journal of Complexity: Volume 36 Issue C, October 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

In 1941, Claude Shannon introduced the General Purpose Analog Computer (GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later on electronic) machines of that time.Following Shannon's arguments, functions generated by the GPAC must satisfy a polynomial differential algebraic ...
Keywords: General Purpose Analog Computer, Analog computation, Continuous-time computations, Real computations

3
November 2015 MACIS 2015: Revised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 9582
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

In this abstract we present a rigorous numerical algorithm which solves initial-value problems IVPs defined with polynomial differential equations i.e.﾿IVPs of the type $$y'=pt,y$$, $$yt_0=y_0$$, where p is a vector of polynomials for any value of t. The inputs of the algorithm are the data defining the initial-value problem, the ...

4
August 2013 Journal of Computer and System Sciences: Volume 79 Issue 5, August, 2013
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 1

This paper analyzes the computational power of dynamical systems robust to infinitesimal perturbations. Previous work on the subject has delved on very specific types of systems. Here we obtain results for broader classes of dynamical systems (including those systems defined by Lipschitz/analytic functions). In particular we show that systems robust ...
Keywords: Reachability, Computational power, Dynamical systems, Robustness, Verification

5
August 2012 MFCS'12: Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 0

We define a general model capturing the behavior of a population of anonymous agents that interact in pairs. This model captures some of the main features of opportunistic networks, in which nodes (such as the ones of a mobile ad hoc networks) meet sporadically. For its reminiscence to Population Protocol, ...

6 published by ACM
July 2012 ISSAC '12: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 0,   Downloads (12 Months): 6,   Downloads (Overall): 55

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In this paper we prove that computing the solution of an initial-value problem y = p ( y ) with initial condition y ( t 0 ) = y 0 ∈ R d at time t 0 + T with precision 2 −μ where p is a vector of polynomials ...

7
May 2012 TAMC'12: Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 0

We propose a formalization of analog algorithms, extending the framework of abstract state machines to continuous-time models of computation.

8
March 2012 Natural Computing: an international journal: Volume 11 Issue 1, March 2012
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 0


9
August 2011 MFCS'11: Proceedings of the 36th international conference on Mathematical foundations of computer science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R n and C n , under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of ...

10
May 2011 Theoretical Computer Science: Volume 412 Issue 22, May, 2011
Publisher: Elsevier Science Publishers Ltd.
Bibliometrics:
Citation Count: 1

We recently obtained partial results on the computational power of population protocols when the population is assumed to be large. We studied in particular a particular protocol that we proved to converge towards 12, using weak-convergence methods for stochastic processes. In this paper, we prove that it is possible to ...
Keywords: Probabilistic analysis, Complexity, Convergence proof, Computability, Probabilistic systems

11
August 2010 MFCS'10: Proceedings of the 35th international conference on Mathematical foundations of computer science
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to infinitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous differential equation systems, discontinuous piecewise affine maps, or perturbed Turing machines), we prove ...
Keywords: verification, analog computations, computable analysis, model-checking

12
October 2009 VALUETOOLS '09: Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Publisher: ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering)
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 0,   Downloads (12 Months): 8,   Downloads (Overall): 94

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We study how to reach a Nash equilibrium in a load balancing scenario where each task is managed by a selfish agent and attempts to migrate to a machine which will minimize its cost. The cost of a machine is a function of the load on it. The load on ...

13
October 2009 Applied Mathematics and Computation: Volume 215 Issue 4, October, 2009
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their ...
Keywords: Population protocols, Computability, Limits

14
August 2008 UC '08: Proceedings of the 7th international conference on Unconventional Computing
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

We consider the problem of learning equilibria in a well known game theoretic traffic model due to Wardrop. We consider a distributed learning algorithm that we prove to converge to equilibria. The proof of convergence is based on a differential equation governing the global macroscopic evolution of the system, inferred ...

15
September 2007 MCU'07: Proceedings of the 5th international conference on Machines, computations, and universality
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 1

We review some results about the computational power of several computational models. Considered models have in common to be related to continuous dynamical systems.

16
June 2007 Journal of Complexity: Volume 23 Issue 3, June, 2007
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 15

In the last decade, there have been several attempts to understand the relations between the many models of analog computation. Unfortunately, most models are not equivalent. Euler's Gamma function, which is computable according to computable analysis, but that cannot be generated by Shannon's General Purpose Analog Computer (GPAC), has often ...
Keywords: Differential equations, General Purpose Analog Computer, Analog computation, Church--Turing thesis, Computable analysis

17
December 2006 Fundamenta Informaticae - SPECIAL ISSUE MCU2004: Volume 74 Issue 4, December 2006
Publisher: IOS Press
Bibliometrics:
Citation Count: 11

Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds ...

18
December 2006 Fundamenta Informaticae - SPECIAL ISSUE MCU2004: Volume 74 Issue 4, December 2006
Publisher: IOS Press
Bibliometrics:
Citation Count: 0

Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds ...

19
August 2006 RTA'06: Proceedings of the 17th international conference on Term Rewriting and Applications
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 2

In last RTA, we introduced the notion of probabilistic rewrite systems and we gave some conditions entailing termination of those systems within a finite mean number of reduction steps. Termination was considered under arbitrary unrestricted policies. Policies correspond to strategies for non-probabilistic rewrite systems. This is often natural or more ...

20
May 2006 TAMC'06: Proceedings of the Third international conference on Theory and Applications of Models of Computation
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 4

In this paper we revisit one of the first models of analog computation, Shannon’s General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPAC-computability in a natural way, we compute ...



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