A Survey on Analog Models of Computation

Bournez, Olivier; Pouly, Amaury

doi:10.48550/arxiv.1805.05729

Cited by 2 publications

(3 citation statements)

References 242 publications

(305 reference statements)

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“…More recently, is has been proved that polynomial differential equations can be considered as a very simple and elegant model in which computable functions over the reals and polynomial time computable functions over the reals can be defined without any reference to concepts from discrete computation theory [5,35]. Refer to [7,6] for an up to date survey about various works on analog computations, in particular in a computation theory perspective.…”

Section: Analog Computationsmentioning

confidence: 99%

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Recursion schemes, discrete differential equations and characterization of polynomial time computation

Bournez,

Durand,

Ouazzani

2018

Preprint

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This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations of complexity and computability classes.The proposed framework presents an original point of view on complexity and computability classes. It also unifies in an elegant settings various constructions that have been proposed for characterizing these classes. This includes Cobham's and, Bellantoni and Cook's definition of polynomial time and later extensions on the approach, as well as recent characterizations of computability and complexity by classes of ordinary differential equations. It also helps understanding the relationships between analog computations and classical discrete models of computation theory.At a more technical point of view, this paper points out the fundamental role of linear (discrete) ordinary differential equations and classical ODE tools such as changes of variables to capture computability and complexity measures, or as a tool for programming various algorithms.

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Section: Analog Computationsmentioning

confidence: 99%

“…Thinking about what means this integral, discrete ODE (21), also encoded by (6), can also be interpreted as tan…”

Section: Discrete Ordinary Differential Equations (Ode)mentioning

confidence: 99%

Recursion schemes, discrete differential equations and characterization of polynomial time computation

Bournez,

Durand,

Ouazzani

2018

Preprint

Self Cite

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“… Bournez and Pouly survey a number of other analog models of computation in a recent review(Bournez and Pouly, 2018) and the reader is referred there for detailed discussion of the full range of models.…”

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confidence: 99%