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Computing with Infinite Data

Computing with Infinite Data

Objective

The joint research in this programme will study important aspects—both theoretical as well as applied—of computing with infinite objects. A central aim is laying the grounds for the generation of efficient and verified software in engineering applications.

A prime example for infinite data is provided by the real numbers, most commonly conceived as infinite sequences of digits. While most applications in science and engineering substitute the reals with floating point numbers of fixed finite precision and thus have to deal with truncation and rounding errors, the approach in this project is different: exact real numbers are taken as first-class citizens and while any computation can only exploit a finite portion of its input in finite time, increased precision is always available by continuing the computation process.

This project aims to bring together the expertise of specialists in mathematics, logic, and computer science to push the frontiers of our theoretical and practical understanding of computing with infinite objects. Three overarching motivations drive the proposed collaboration:

Representability. Cardinality considerations tell us that it is not possible to represent arbitrary mathematical objects in a way that is accessible to computation. We will enlist expertise in topology, logic, and set theory, to address the question of which objects are representable and how they can be represented most efficiently.

Constructivity. Working in a constructive mathematical universe can greatly enhance our understanding of the link between computation and mathematical structure. Not only informs us which are the objects of relevance, it also allows us to devise always correct algorithms from proofs.

Efficient implementation. We also aim to make progress on concrete implementations. Theoretical insights from elsewhere will be tested in actual computer systems; obstacles encountered in the latter will inform the direction of mathematical investigation.
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Coordinator

UNIVERSITAET SIEGEN

Address

Adolf Reichwein Strasse 2a
57076 Siegen

Germany

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 72 000

Participants (12)

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UNIVERSITAT TRIER

Germany

EU Contribution

€ 76 500

LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN

Germany

EU Contribution

€ 207 000

SWANSEA UNIVERSITY

United Kingdom

EU Contribution

€ 112 500

THE UNIVERSITY OF BIRMINGHAM

United Kingdom

EU Contribution

€ 90 000

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE

France

EU Contribution

€ 90 000

UNIVERZA V LJUBLJANI

Slovenia

EU Contribution

€ 58 500

UNIVERSITEIT MAASTRICHT

Netherlands

EU Contribution

€ 18 000

STOCKHOLMS UNIVERSITET

Sweden

EU Contribution

€ 40 500

UNIVERSITA DEGLI STUDI DI PADOVA

Italy

EU Contribution

€ 72 000

UNIVERSIDADE DO ALGARVE

Portugal

EU Contribution

€ 58 500

ASTON UNIVERSITY

United Kingdom

EU Contribution

€ 27 000

Fachhochschule Dortmund

Germany

EU Contribution

€ 36 000

Partners (8)

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UNIVERSITY OF SOUTH AFRICA

UNIVERSIDAD ANDRES BELLO

KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY

NATIONAL UNIVERSITY CORPORATION JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY

INSTITUTION OF THE RUSSIAN ACADEMY OF SCIENCES A.P. ERSHOV INSTITUTE OF INFORMATICS SYSTEMS SIBERIAN BRANCH OF RAS

UNIVERSITY OF CANTERBURY

University of Cincinnati

NANYANG TECHNOLOGICAL UNIVERSITY

Project information

Grant agreement ID: 731143

Status

Ongoing project

  • Start date

    1 April 2017

  • End date

    31 March 2021

Funded under:

H2020-EU.1.3.3.

  • Overall budget:

    € 1 462 500

  • EU contribution

    € 958 500

Coordinated by:

UNIVERSITAET SIEGEN

Germany