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 …

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 …

A foundation for real recursive function theory

JF Costa, B Loff, J Mycka - Annals of Pure and Applied Logic, 2009 - Elsevier
The class of recursive functions over the reals, denoted by REC (R), was introduced by
Cristopher Moore in his seminal paper written in 1995. Since then many subsequent …

Differential recursion

A Kawamura - ACM Transactions on Computational Logic (TOCL), 2009 - dl.acm.org
We present a redevelopment of the theory of real-valued recursive functions that was
introduced by C. Moore in 1996 by analogy with the standard formulation of the integer …

[PDF][PDF] A functional characterisation of the analytical hierarchy

B Loff - Computability in Europe, 2007 - cmaf.fc.ul.pt
We study an inductive class of vector functions over the reals, defined from a set of basic
functions by composition, solving of first order differential equations and the taking of infinite …

[PDF][PDF] Algebraic Characterizations of Computable Analysis Real Functions.

W Gomaa - Int. J. Unconv. Comput., 2011 - researchgate.net
The extended class can exactly characterize discrete polynomial time computation,
however, can only partially characterize polynomial time real computation. Furthermore …

[PDF][PDF] Rational vs. Real Computation.

W Gomaa - Int. J. Softw. Informatics, 2013 - academia.edu
There have been several different approaches of investigating computation over the real
numbers. Among such computable analysis seems to be the most amenable to physical …

Polynomial time computation in the context of recursive analysis

W Gomaa - International Workshop on Foundational and Practical …, 2009 - Springer
Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D.
Lacombe [1955] as an approach for investigating computation over the real numbers. It is …

A survey of recursive analysis and Moore's notion of real computation

W Gomaa - Natural Computing, 2012 - Springer
The theory of analog computation aims at modeling computational systems that evolve in a
continuous space. Unlike the situation with the discrete setting there is no unified theory of …

A survey on continuous time computations

O Bournez, M Campagnolo - arxiv preprint arxiv:0907.3117, 2009 - arxiv.org
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 …