On the Computational Capabilities of Several Models

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On the Computational Capabilities of Several Models
We review some results about the computational power of several computational models. Considered models have in common to be related to continuous dynamical systems. 1 Dynamical Systems and Polynomial Cauchy Problems A polynomial Cauchy problem is a Cauchy problem of type x = p(x, t) x(0) = x0 where p(x, t) is a vector of polynomials, and x0 is some initial condition. The class of functions that are solution of a polynomial Cauchy problem turns out to be a very robust class [14]. It contains almost all natural mathematical functions. It is closed under addition, subtraction, multiplication, division, composition, differentiation, and compositional inverse [14]. Actually, every continuous time dynamical system x = f(x, t) where each component of f is defined as a composition of functions in the class and polynomials can be shown equivalent to a (possibly higher dimensional) polynomial Cauchy problem [14]. This implies that almost all continuous time dynamical systems considered in boo...
Olivier Bournez, Emmanuel Hainry
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2007
Where MCU
Authors Olivier Bournez, Emmanuel Hainry
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