Section: New Results

Highlights of the Year

Our team made remarkable progress into the understanding of complexity of higher-order functionals. While a robust class of computable functionals exists at any finite type built from $\mathbb{N}$ and $\to$ (the Kleene-Kreisel functionals), no satisfying complexity classes had been defined so far, except the class BFF of Basic Feasible Functionals. However that class is not a complexity class in the usual sense and does not offer the possibility to define space complexity or non-deterministic time complexity. In his PhD Hugo Férée has developed a non-trivial notion of size for higher-order functionals using game semantics and he has defined a notion of polynomial-time computable functional including BFF but behaving more satisfactorily in several ways. A paper in preparation will gather these results.