In this paper, we derive from these results the strong (uniform computability) Turing completeness of chemical reaction networks over a finite set of molecular species under the differential semantics .Expand

The outcomes of this article are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the… Expand

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions).Expand

The Orbit Problem consists of determining, given a linear transformation A on d-dimensional rationals Q^d, together with vectors x and y, whether the orbit of x under repeated applications of A can ever reach y.Expand

We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides, which is then truncated to obtain a finite-dimensional representation with additive error.Expand

In this paper we investigate the computational complexity of solving ordinary differential equations (ODEs) over unbounded time domains, where p is a vector of polynomials.Expand

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 continuous-time analog (mechanical, and later electronic) machines of that time.Expand

Nonlinear dynamical systems abound as models of natural phenomena. They are often characterized by highly unpredictable behaviour which is hard to analyze as it occurs, for example, in chaotic… Expand

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine, as long as we are talking about bounded computations.Expand

We show that whether a given instance of the Orbit Problem admits a semialgebraic invariant is decidable, and moreover in positive instances we provide an algorithm to synthesise suitable succinct invariants of polynomial size.Expand