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 …
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 …
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 …
A characterization of functions over the integers computable in polynomial time using discrete ordinary differential equations
O Bournez, A Durand - computational complexity, 2023 - Springer
This paper studies the expressive and computational power of discrete Ordinary Differential
Equations (ODEs), aka (Ordinary) Difference Equations. It presents a new framework using …
Equations (ODEs), aka (Ordinary) Difference Equations. It presents a new framework using …
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 …
Robust non-computability of dynamical systems and computability of robust dynamical systems
DS Graça, N Zhong - Logical Methods in Computer Science, 2024 - lmcs.episciences.org
In this paper, we examine the relationship between the stability of the dynamical system
x′= f (x) and the computability of its basins of attraction. We present a computable C∞ …
x′= f (x) and the computability of its basins of attraction. We present a computable C∞ …
Robust simulations of Turing machines with analytic maps and flows
LNCS 3526 - Robust Simulations of Turing Machines with Analytic Maps and Flows Page 1
Robust Simulations of Turing Machines with Analytic Maps and Flows * Daniel S. Graça 1,2,⋆⋆ …
Robust Simulations of Turing Machines with Analytic Maps and Flows * Daniel S. Graça 1,2,⋆⋆ …
Real recursive functions and their hierarchy
J Mycka, JF Costa - Journal of Complexity, 2004 - Elsevier
In the last years, recursive functions over the reals (Theoret. Comput. Sci. 162 (1996) 23)
have been considered, first as a model of analog computation, and second to obtain analog …
have been considered, first as a model of analog computation, and second to obtain analog …