Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
- E. Asarin, T. Dang, O. Maler, Olivier Bournez
- MathematicsInternational Conference on Hybrid Systems…
- 23 March 2000
In this paper we describe an experimental system called d/dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an…
Proving Positive Almost-Sure Termination
- Olivier Bournez, Florent Garnier
- Computer ScienceInternational Conference on Rewriting Techniques…
- 19 April 2005
This work provides several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules, including classical ones for non-probabilistic systems.
Effective synthesis of switching controllers for linear systems
- E. Asarin, Olivier Bournez, T. Dang, O. Maler, A. Pnueli
- Computer Science, MathematicsProceedings of the IEEE
- 1 July 2000
A novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations is suggested and an abstract algorithm that solves the problem by an iterative computation of reachable states is proposed.
Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs
- F. Fages, Guillaume Le Guludec, Olivier Bournez, Amaury Pouly
- Computer ScienceComputational Methods in Systems Biology
- 27 September 2017
The strong (uniform computability) Turing completeness of chemical reaction networks over a finite set of molecular species under the differential semantics is derived, solving a long standing open problem.
Orthogonal Polyhedra: Representation and Computation
- Olivier Bournez, O. Maler, A. Pnueli
- Mathematics, Computer ScienceInternational Conference on Hybrid Systems…
- 29 March 1999
This paper defines representation schemes for orthogonal polyhedra based on their vertices, and shows that these compact representation schemes are canonical for all (convex and non- Convex)polyhedra in any dimension.
The Mortality Problem for Matrices of Low Dimensions
- Olivier Bournez, M. Branicky
- Mathematics, Computer ScienceTheory of Computing Systems
- 1 August 2002
The problem to be BSS-undecidable for real matrices and Turing-decidable for two rational matrices is proved and some NP-completeness results are state.
Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
- Olivier Bournez, D. Graça, Amaury Pouly
- Computer Science, MathematicsJournal of the ACM
- 20 January 2016
This result provides arguments in favour of a generalised form of the Church-Turing Hypothesis, which states that any physically realistic (macroscopic) computer is equivalent to Turing machines both in terms of computability and complexity.
Recursive Analysis Characterized as a Class of Real Recursive Functions
- Olivier Bournez, Emmanuel Hainry
- Computer Science, MathematicsFundamenta Informaticae
- 1 December 2006
It is proved that computable functions over the real numbers in the sense of recursive analysis can be characterized as the smallest class of functions that contains some basic functions, and closed by composition, linear integration, minimalization and limit schema.
Deciding stability and mortality of piecewise affine dynamical systems
- V. Blondel, Olivier Bournez, P. Koiran, C. Papadimitriou, J. Tsitsiklis
- MathematicsTheoretical Computer Science
- 28 March 2001
Probabilistic Rewrite Strategies. Applications to ELAN
- Olivier Bournez, C. Kirchner
- Computer ScienceInternational Conference on Rewriting Techniques…
- 22 July 2002
An extension of the ELAN strategy language to deal with randomized systems is proposed, and it is argued through several examples that a natural setting to model systems with randomized choices is proposed.
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