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Competing Provers Yield Improved Karp-Lipton Collapse Results

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

Via competing provers, we show that if a language A is selfreducible and has polynomial-size circuits then SA 2 = S2. Building on this, we strengthen the Kämper-AFK Theorem, namely, we prove that if NP ⊆ (NP ∩coNP)/poly then the polynomial hierarchy collapses to SNP∩coNP 2 . We also strengthen Yap’s Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to SNP 2 . Under the same assumptions, the best previously known collapses were to ZPPNP and ZPPNP NP respectively ([20],[6], building on [18,1,17,30]). It is known that S2 ⊆ ZPPNP [8]. That result and its relativized version show that our new collapses indeed improve the previously known results. Since the Kämper-AFK Theorem and Yap’s Theorem are used in the literature as bridges in a variety of results-ranging from the study of unique solutions to issues of approximation-our results implicitly strengthen all those results.

Supported in part by NIH grants RO1-AG18231 and P30-AG18254, and NSF grants CCR-9322513, INT-9726724, CCR-9701911, INT-9815095, DUE-9980943, EIA-0080124, CCR-0196197, and EIA-0205061.

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Author information

Authors and Affiliations

  1. Comp. Sci. Dept., Univ. of Wisc., 53706, Madison, WI

    Jin-Yi Cai & Venkatesan T. Chakaravarthy

  2. Dept. of Comp. Sci., Univ. of Rochester, 14627, Rochester, NY

    Lane A. Hemaspaandra & Mitsunori Ogihara

Authors
  1. Jin-Yi Cai
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  2. Venkatesan T. Chakaravarthy
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  3. Lane A. Hemaspaandra
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  4. Mitsunori Ogihara
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Cai, JY., Chakaravarthy, V.T., Hemaspaandra, L.A., Ogihara, M. (2003). Competing Provers Yield Improved Karp-Lipton Collapse Results. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_47

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  • DOI: https://doi.org/10.1007/3-540-36494-3_47

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  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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