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Computational complexity with experiments as oracles

Edwin Beggs Orcid Logo, José Félix Costa, Bruno Loff, John Tucker Orcid Logo

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume: 464, Issue: 2098, Pages: 2777 - 2801

Swansea University Authors: Edwin Beggs Orcid Logo, John Tucker Orcid Logo

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DOI (Published version): 10.1098/rspa.2008.0085

Abstract

We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of AD machine are...

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Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1471-2946
Published: London The Royal Society 2008
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa7205
first_indexed 2013-07-23T11:57:35Z
last_indexed 2018-02-09T04:35:07Z
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spelling 2015-10-15T10:30:07.0465773 v2 7205 2012-02-23 Computational complexity with experiments as oracles a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 431b3060563ed44cc68c7056ece2f85e 0000-0003-4689-8760 John Tucker John Tucker true false 2012-02-23 MACS We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of AD machine are studied, in which physical parameters can be set exactly and approximately. Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines. Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464 2098 2777 2801 The Royal Society London 1471-2946 algorithmic procedure; experimental procedure; Turing machines with oracles; analogue–digital computation; non-uniform complexity 31 12 2008 2008-12-31 10.1098/rspa.2008.0085 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2015-10-15T10:30:07.0465773 2012-02-23T17:01:48.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Edwin Beggs 0000-0002-3139-0983 1 José Félix Costa 2 Bruno Loff 3 John Tucker 0000-0003-4689-8760 4
title Computational complexity with experiments as oracles
spellingShingle Computational complexity with experiments as oracles
Edwin Beggs
John Tucker
title_short Computational complexity with experiments as oracles
title_full Computational complexity with experiments as oracles
title_fullStr Computational complexity with experiments as oracles
title_full_unstemmed Computational complexity with experiments as oracles
title_sort Computational complexity with experiments as oracles
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
431b3060563ed44cc68c7056ece2f85e
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
431b3060563ed44cc68c7056ece2f85e_***_John Tucker
author Edwin Beggs
John Tucker
author2 Edwin Beggs
José Félix Costa
Bruno Loff
John Tucker
format Journal article
container_title Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
container_volume 464
container_issue 2098
container_start_page 2777
publishDate 2008
institution Swansea University
issn 1471-2946
doi_str_mv 10.1098/rspa.2008.0085
publisher The Royal Society
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description We discuss combining physical experiments with machine computations and introduce a form of analogue–digital (AD) Turing machine. We examine in detail a case study where an experimental procedure based on Newtonian kinematics is combined with a class of Turing machines. Three forms of AD machine are studied, in which physical parameters can be set exactly and approximately. Using non-uniform complexity theory, and some probability, we prove theorems that show that these machines can compute more than classical Turing machines.
published_date 2008-12-31T12:16:15Z
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score 10.958922

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