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In this paper, we show that closed-form analytic maps and flows can simulate Turing machines in an error-robust manner. The maps and ODEs defining the flows are explicitly obtained and the simulation… (More)

Let (α, β) ⊆ R denote the maximal interval of existence of solutions for the initial-value problem { dx dt = f(t, x), x(t0) = x0, where E is an open subset of Rm+1, f is continuous in E and (t0, x0)… (More)

- Daniel S. Graça
- 2018

In this paper we compare computational power of two models of analog and classical computers. As a model of analog computer we use the model proposed by Rubel in 1993 called the Extended Analog… (More)

In this paper we revisit one of the first models of analog computation, Shannon’s General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main… (More)

- Pieter Collins, Daniel S. Graça
- Electr. Notes Theor. Comput. Sci.
- 2008

In this note we consider the computability of the solution of the initial-value problem for ordinary differential equations with continuous right-hand side. We present algorithms for the computation… (More)

- Olivier Bournez, Daniel S. Graça, Amaury Pouly
- Inf. Comput.
- 2017

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… (More)

- Daniel S. Graça, Ning Zhong
- UC
- 2009

In this note we investigate the problem of computing the domain of attraction of a flow on R for a given attractor. We consider an operator that takes two inputs, the description of the flow and a… (More)

In this paper, we show that there are Initial Value Problems defined with polynomial ordinary differential equations that can simulate universal Turing machines in the presence of bounded noise. The… (More)

- Olivier Bournez, Daniel S. Graça, Amaury Pouly
- MFCS
- 2011

In this paper we consider the computational complexity of solving initial-value problems defined with analytic ordinary differential equations (ODEs) over unbounded domains of R and C, under the… (More)

- Daniel S. Graça, Jorge Buescu, Manuel Lameiras Campagnolo
- Applied Mathematics and Computation
- 2009

In this paper we study from a computational perspective some properties of the solutions of polynomial ordinary differential equations. We consider elementary (in the sense of Analysis) discrete-time… (More)