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One Bit of Advice

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STACS 2003 (STACS 2003)

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

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Abstract

The results in this paper show that coNP is contained in NP with 1 bit of advice (denoted NP/1) if and only if the Polynomial Hierarchy (PH) collapses to DP, the second level of the Boolean Hierarchy (BH). Previous work showed that BH ∶DP⇒ coNP ∶ NP/poly. The stronger assumption that PH ∶ DP in the new result allows the length of the advice function to be reduced to a single bit and also makes the converse true. The one-bit case can be generalized to any constant k: PH ∶ BH2k ⇔ coNP ∶ NP/k

where BH2k denotes the 2k-th level of BH and NP/k denotes the class NP with k-bit advice functions.

Supported in part by the University of Maryland Institute for Advanced Computer Studies.

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Author information

Authors and Affiliations

  1. CWI & University of Amsterdam, CWI, INS4, P.O. Box 94709, Amsterdam, The Netherlands

    Harry Buhrman

  2. Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, 21250, Baltimore, MD, USA

    Richard Chang

  3. NEC Laboratories America, 4 Independence Way, 08540, Princeton, NJ, USA

    Lance Fortnow

Authors
  1. Harry Buhrman
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  2. Richard Chang
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  3. Lance Fortnow
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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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© 2003 Springer-Verlag Berlin Heidelberg

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Buhrman, H., Chang, R., Fortnow, L. (2003). One Bit of Advice. 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_48

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  • DOI: https://doi.org/10.1007/3-540-36494-3_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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