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...

• Type: Conference
• Year: 2007
• Where: MCU
• Authors: Olivier Bournez, Emmanuel Hainry
• Keywords: Continuous Dynamical Systems, Dynamical Systems, Hardware, MCU 2007, Polynomial Cauchy Problems