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International Colloquium on Automata, Languages, and Programming

ICALP 2002: Automata, Languages and Programming pp 208–219Cite as

Bounded-Depth Frege Systems with Counting Axioms Polynomially Simulate Nullstellensatz Refutations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

Abstract

We show that bounded-depth Frege systems with counting axioms modulo m polynomially simulate Nullstellensatz refutations modulo m. When combined with a previous result of the authors, this establishes the first size (as opposed to degree) separation between Nullstellensatz and polynomial calculus refutations.

Research Supported by NSF Award CCR-9734911, grant #93025 of the joint US-Czechoslovak Science and Technology Program, NSF Award CCR-0098197, and USA-Israel BSF Grant 97-00188

Partially supported by NSF grant DMS-9803515

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, San Diego La Jolla, CA, 92093

    Russell Impagliazzo & Nathan Segerlind

Authors
  1. Russell Impagliazzo
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  2. Nathan Segerlind
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

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© 2002 Springer-Verlag Berlin Heidelberg

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Impagliazzo, R., Segerlind, N. (2002). Bounded-Depth Frege Systems with Counting Axioms Polynomially Simulate Nullstellensatz Refutations. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_19

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  • DOI: https://doi.org/10.1007/3-540-45465-9_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

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