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The Ordering Principle in a Fragment of Approximate Counting

The Ordering Principle in a Fragment of Approximate Counting The Ordering Principle in a Fragment of Approximate Counting ALBERT ATSERIAS, Universitat Polit` cnica de Catalunya, Barcelona e NEIL THAPEN, Academy of Sciences of the Czech Republic, Prague The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over T1 . This answers an open question raised in Buss 2 et al. [2012] and completes their program to compare the strength of Je abek's bounded arithmetic theory r´ for approximate counting with weakened versions of it. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Complexity of proof procedures; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic--Proof theory General Terms: Theory, Algorithms Additional Key Words and Phrases: Computational complexity, bounded arithmetic, propositional proof complexity, polynomial local search ACM Reference Format: Albert Atserias and Neil Thapen. 2014. The ordering principle in a fragment of approximate counting. ACM Trans. Comput. Logic 15, 4, Article 29 (November 2014), 11 pages. DOI: http://dx.doi.org/10.1145/2629555 1. INTRODUCTION We show that, in the relativized setting, the surjective weak pigeonhole principle for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

The Ordering Principle in a Fragment of Approximate Counting

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2629555
Publisher site
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Abstract

The Ordering Principle in a Fragment of Approximate Counting ALBERT ATSERIAS, Universitat Polit` cnica de Catalunya, Barcelona e NEIL THAPEN, Academy of Sciences of the Czech Republic, Prague The ordering principle states that every finite linear order has a least element. We show that, in the relativized setting, the surjective weak pigeonhole principle for polynomial time functions does not prove a Herbrandized version of the ordering principle over T1 . This answers an open question raised in Buss 2 et al. [2012] and completes their program to compare the strength of Je abek's bounded arithmetic theory r´ for approximate counting with weakened versions of it. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Complexity of proof procedures; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic--Proof theory General Terms: Theory, Algorithms Additional Key Words and Phrases: Computational complexity, bounded arithmetic, propositional proof complexity, polynomial local search ACM Reference Format: Albert Atserias and Neil Thapen. 2014. The ordering principle in a fragment of approximate counting. ACM Trans. Comput. Logic 15, 4, Article 29 (November 2014), 11 pages. DOI: http://dx.doi.org/10.1145/2629555 1. INTRODUCTION We show that, in the relativized setting, the surjective weak pigeonhole principle for

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ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Nov 7, 2014

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