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Journal article 1734 views

Uniform Proof Complexity

A Beckmann, Arnold Beckmann Orcid Logo

Journal of Logic and Computation, Volume: 15, Issue: 4, Pages: 433 - 446

Swansea University Author: Arnold Beckmann Orcid Logo

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DOI (Published version): 10.1093/logcom/exi035

Abstract

We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform...

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Published in: Journal of Logic and Computation
ISSN: 0955-792X 1465-363X
Published: 2005
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URI: https://cronfa.swan.ac.uk/Record/cronfa1702
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spelling 2013-10-17T11:47:49.8727947 v2 1702 2011-10-01 Uniform Proof Complexity 1439ebd690110a50a797b7ec78cca600 0000-0001-7958-5790 Arnold Beckmann Arnold Beckmann true false 2011-10-01 MACS We define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are \Pi^0_1-hard and obviously in \Sigma^0_2. We also show under certain regularity conditions that each uniform reduct is closed under bounded generalisation; that in the case the language includes a symbol for exponentiation, a uniform reduct is closed under modus ponens if and only if it already contains all true bounded formulas; and that each uniform reduct contains all true \Pi^b_1(\alpha)-formulas. Journal Article Journal of Logic and Computation 15 4 433 446 0955-792X 1465-363X 4 8 2005 2005-08-04 10.1093/logcom/exi035 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2013-10-17T11:47:49.8727947 2011-10-01T00:00:00.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science A Beckmann 1 Arnold Beckmann 0000-0001-7958-5790 2
title Uniform Proof Complexity
spellingShingle Uniform Proof Complexity
Arnold Beckmann
title_short Uniform Proof Complexity
title_full Uniform Proof Complexity
title_fullStr Uniform Proof Complexity
title_full_unstemmed Uniform Proof Complexity
title_sort Uniform Proof Complexity
author_id_str_mv 1439ebd690110a50a797b7ec78cca600
author_id_fullname_str_mv 1439ebd690110a50a797b7ec78cca600_***_Arnold Beckmann
author Arnold Beckmann
author2 A Beckmann
Arnold Beckmann
format Journal article
container_title Journal of Logic and Computation
container_volume 15
container_issue 4
container_start_page 433
publishDate 2005
institution Swansea University
issn 0955-792X
1465-363X
doi_str_mv 10.1093/logcom/exi035
college_str Faculty of Science and Engineering
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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 define the notion of the uniform reduct of a propositional proof system as the set of those bounded formulas in the language of Peano Arithmetic which have polynomial size proofs under the Paris-Wilkie-translation. With respect to the arithmetic complexity of uniform reducts, we show that uniform reducts are \Pi^0_1-hard and obviously in \Sigma^0_2. We also show under certain regularity conditions that each uniform reduct is closed under bounded generalisation; that in the case the language includes a symbol for exponentiation, a uniform reduct is closed under modus ponens if and only if it already contains all true bounded formulas; and that each uniform reduct contains all true \Pi^b_1(\alpha)-formulas.
published_date 2005-08-04T03:06:55Z
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score 11.089407

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