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Error-Bounded Probabilistic Computations between MA and AM

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Mathematical Foundations of Computer Science 2003 (MFCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2747))

Abstract

We introduce the probabilistic complexity class SBP. This class emerges from BPP by keeping the promise of a probability gap but decreasing the probability limit to exponentially small values. We locate SBP in the polynomial-time hierarchy, more precisely, between MA and AM. We provide evidence that SBP does not coincide with these and other known complexity classes. We construct an oracle relative to which SBP is not contained in \({\mathrm{\Sigma^P_{2}}}\).

We provide a new characterization of BPPpath. This characterization shows that SBP is a subset of BPPpath. Consequently, there is an oracle relative to which BPPpath is not contained in \({\mathrm{\Sigma^P_{2}}}\).

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Würzburg, 97074, Würzburg, Germany

    Elmar Böhler, Christian Glaßer & Daniel Meister

Authors
  1. Elmar Böhler
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  2. Christian Glaßer
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  3. Daniel Meister
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Branislav Rovan

  2. Charles University, Prague, Czech Republic

    Peter Vojtáš

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Böhler, E., Glaßer, C., Meister, D. (2003). Error-Bounded Probabilistic Computations between MA and AM. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_19

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  • DOI: https://doi.org/10.1007/978-3-540-45138-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40671-6

  • Online ISBN: 978-3-540-45138-9

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