42 citations · 109 across the 13 of their papers we have counts for
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On the Functions Generated by the General Purpose Analog Computer
Olivier Bournez, Daniel Graça, Amaury Pouly
We consider the General Purpose Analog Computer (GPAC), introduced by Claude Shannon in 1941 as a mathematical model of Differential Analysers, that is to say as a model of continu…
Computing with Polynomial Ordinary Differential Equations
Olivier Bournez, Daniel Graça, Amaury Pouly
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…
Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
Olivier Bournez, Daniel S. Graça, Amaury Pouly
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class of languages co…
Computational complexity of solving polynomial differential equations over unbounded domains
Amaury Pouly, Daniel S. Graça
In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) over \emph{unbounded time domains}, where is a vec…
Turing machines can be efficiently simulated by the General Purpose Analog Computer
Amaury Pouly, Olivier Bournez, Daniel S. Graça
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This…