42 citations · 109 across the 13 of their papers we have counts for
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cs.CC2016
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…
cs.CC2016★ 12 cited
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…
cs.CC2016★ 42 cited
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…