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An unexpected separation result in Linearly Bounded Arithmetic

Arnold Beckmann Orcid Logo, Jan Johannsen

MLQ, Volume: 51, Issue: 2, Pages: 191 - 200

Swansea University Author: Arnold Beckmann Orcid Logo

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DOI (Published version): 10.1002/malq.200410019

Abstract

The theories S i 1 (α) and T i 1 (α) are the analogues of Buss' relativized bounded arithmetic theories in the language where every term is bounded by a polynomial, and thus all definable functions grow linearly in length. For every i , a Σ b i+1 (α) - formula TOPi(α) , which expresses a form o...

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Published in: MLQ
ISSN: 0942-5616 1521-3870
Published: 2005
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URI: https://cronfa.swan.ac.uk/Record/cronfa13721
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spelling 2013-10-17T11:49:10.7665259 v2 13721 2012-12-17 An unexpected separation result in Linearly Bounded Arithmetic 1439ebd690110a50a797b7ec78cca600 0000-0001-7958-5790 Arnold Beckmann Arnold Beckmann true false 2012-12-17 SCS The theories S i 1 (α) and T i 1 (α) are the analogues of Buss' relativized bounded arithmetic theories in the language where every term is bounded by a polynomial, and thus all definable functions grow linearly in length. For every i , a Σ b i+1 (α) - formula TOPi(α) , which expresses a form of the total ordering principle, is exhibited that is provable in S i+1 1 (α) , but unprovable in T i 1 (α) . This is in contrast with the classical situation, where S i+1 2 is conservative over T i 2 w.r.t. Σ b i+1 -sentences. The independence results are proved by translations into propositional logic, and using lower bounds for corresponding propositional proof systems. Journal Article MLQ 51 2 191 200 0942-5616 1521-3870 31 12 2005 2005-12-31 10.1002/malq.200410019 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2013-10-17T11:49:10.7665259 2012-12-17T10:23:38.0962755 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Arnold Beckmann 0000-0001-7958-5790 1 Jan Johannsen 2
title An unexpected separation result in Linearly Bounded Arithmetic
spellingShingle An unexpected separation result in Linearly Bounded Arithmetic
Arnold Beckmann
title_short An unexpected separation result in Linearly Bounded Arithmetic
title_full An unexpected separation result in Linearly Bounded Arithmetic
title_fullStr An unexpected separation result in Linearly Bounded Arithmetic
title_full_unstemmed An unexpected separation result in Linearly Bounded Arithmetic
title_sort An unexpected separation result in Linearly Bounded Arithmetic
author_id_str_mv 1439ebd690110a50a797b7ec78cca600
author_id_fullname_str_mv 1439ebd690110a50a797b7ec78cca600_***_Arnold Beckmann
author Arnold Beckmann
author2 Arnold Beckmann
Jan Johannsen
format Journal article
container_title MLQ
container_volume 51
container_issue 2
container_start_page 191
publishDate 2005
institution Swansea University
issn 0942-5616
1521-3870
doi_str_mv 10.1002/malq.200410019
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
document_store_str 0
active_str 0
description The theories S i 1 (α) and T i 1 (α) are the analogues of Buss' relativized bounded arithmetic theories in the language where every term is bounded by a polynomial, and thus all definable functions grow linearly in length. For every i , a Σ b i+1 (α) - formula TOPi(α) , which expresses a form of the total ordering principle, is exhibited that is provable in S i+1 1 (α) , but unprovable in T i 1 (α) . This is in contrast with the classical situation, where S i+1 2 is conservative over T i 2 w.r.t. Σ b i+1 -sentences. The independence results are proved by translations into propositional logic, and using lower bounds for corresponding propositional proof systems.
published_date 2005-12-31T03:14:14Z
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