3 papers
cs.SC2026
Relating the Computational and Logical Difficulty of Solving ODEs: From Polynomial to Discontinuous Right-Hand Sides
Olivier Bournez, Alonso Núñez
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions be…
cs.CC2026
Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
Olivier Bournez
What do recurrent neural networks, polynomial ODEs, and discrete polynomial maps each bring to computation, and what do they lack? All three operate over the continuum--real-valued…
math.LO2025
Toward higher-order infinite time Turing machines: simulational -machines
Olivier Bournez, Olivier Finkel, Johan Girardot
Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which…