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 …
Analog Computer (GPAC). In particular, we restrict our attention to the improved model …
[HTML][HTML] Analog computers and recursive functions over the reals
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 …
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
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 …
the many models of analog computation. Unfortunately, most models are not equivalent …
Computability with polynomial differential equations
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 …
differential equations that can simulate universal Turing machines in the presence of …
A survey on analog models of computation
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 …
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
A continuous characterization of PSPACE using polynomial ordinary differential equations -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …
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 …
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
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 …
Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than …
An analog characterization of the Grzegorczyk hierarchy
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 …
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 …
namely the General Purpose Analog Computer (GPAC). The GPAC is a physically feasible …