• Publications
  • Influence
Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs
TLDR
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
  • 37
  • 6
Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length
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 theExpand
  • 18
  • 3
  • PDF
Polynomial Invariants for Affine Programs
TLDR
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
  • 19
  • 2
  • PDF
Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem
TLDR
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
  • 6
  • 2
  • PDF
Explicit Error Bounds for Carleman Linearization
TLDR
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
  • 5
  • 2
  • PDF
Computational complexity of solving polynomial differential equations over unbounded domains with non-rational coefficients
  • A. Pouly
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 1 September 2014
TLDR
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
  • 15
  • 1
  • PDF
On the Functions Generated by the General Purpose Analog Computer
TLDR
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
  • 12
  • 1
  • PDF
Computability and Computational Complexity of the Evolution of Nonlinear Dynamical Systems
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 chaoticExpand
  • 5
  • 1
  • PDF
Turing Machines Can Be Efficiently Simulated by the General Purpose Analog Computer
TLDR
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
  • 5
  • 1
  • PDF
Complete Semialgebraic Invariant Synthesis for the Kannan-Lipton Orbit Problem
TLDR
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
  • 3
  • 1