Emmanuel Hainry

We prove 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. Expand

We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: they correspond to the smallest class of functions that contains some basic functions, and closed by composition, linear integration, and a simple limit schema. Expand

We show that the Skolem-Pisot problem that is undecidable in the general case is in fact decidable for a natural class of continuous-time dynamical systems: linear systems. Expand

We show that, in an appropriate framework, the GPAC and computable analysis are actually equivalent from the computability point of view, at least in compact intervals. Expand

We extend this result to all computable functions: functions over the reals that extend total recursive functions over integers are proved to correspond to the smallest class of real functions containing some basic functions and closed by composition, linear integration and a natural unique minimization schema. Expand

We present an analog and machine-independent algebraic characterization of elementarily computable functions over the real numbers in the sense of recursive analysis: we prove that they correspond to the smallest class of functions that contains some basic functions and closed by composition, linear integration, and a simple limit schema. Expand

We show that if we change the notion of GPAC-computability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Expand

We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). Expand

We introduce a type system for concurrent programs described as a parallel imperative language using while loops and fork/wait instructions, in which processes do not share a global memory, in order to analyze computational complexity. Expand

This paper provides a criterion based on interpretation methods on term rewrite systems in order to characterize the polynomial time complexity of second order functionals. Expand