Some recent developments on Shannon's general purpose analog computer

D Silva Graça - Mathematical Logic Quarterly: Mathematical …, 2004 - Wiley Online Library
This paper revisits one of the first models of analog computation, the General Purpose
Analog Computer (GPAC). In particular, we restrict our attention to the improved model …

[HTML][HTML] Analog computers and recursive functions over the reals

DS Graça, JF Costa - Journal of Complexity, 2003 - Elsevier
In this paper we show that Shannon's general purpose analog computer (GPAC) is
equivalent to a particular class of recursive functions over the reals with the flavour of …

Polynomial differential equations compute all real computable functions on computable compact intervals

O Bournez, ML Campagnolo, DS Graça, E Hainry - Journal of Complexity, 2007 - Elsevier
In the last decade, there have been several attempts to understand the relations between
the many models of analog computation. Unfortunately, most models are not equivalent …

Computability with polynomial differential equations

DS Graça, ML Campagnolo, J Buescu - Advances in Applied Mathematics, 2008 - Elsevier
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 …

A survey on analog models of computation

O Bournez, A Pouly - Handbook of Computability and Complexity in …, 2021 - Springer
A Survey on Analog Models of Computation Page 1 Chapter 6 A Survey on Analog Models of
Computation Olivier Bournez and Amaury Pouly Abstract We present a survey on analog …

[HTML][HTML] A continuous characterization of PSPACE using polynomial ordinary differential equations

O Bournez, R Gozzi, DS Graça, A Pouly - Journal of Complexity, 2023 - Elsevier
A continuous characterization of PSPACE using polynomial ordinary differential equations -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …

A survey on continuous time computations

O Bournez, ML Campagnolo - New computational paradigms: Changing …, 2008 - Springer
We provide an overview of theories of continuous time computation. These theories allow us
to understand both the hardness of questions related to continuous time dynamical systems …

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

O Bournez, ML Campagnolo, DS Graça… - … Conference on Theory …, 2006 - Springer
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 …

An analog characterization of the Grzegorczyk hierarchy

ML Campagnolo, C Moore, JF Costa - Journal of Complexity, 2002 - Elsevier
We study a restricted version of Shannon's general purpose analog computer in which we
only allow the machine to solve linear differential equations. We show that if this computer is …

Continuous models of computation: from computability to complexity

A Pouly - 2015 - pastel.hal.science
In 1941, Claude Shannon introduced a continuous-time analog model of computation,
namely the General Purpose Analog Computer (GPAC). The GPAC is a physically feasible …