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Structure of complexity classes: Separations, collapses, and completeness

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Mathematical Foundations of Computer Science 1988 (MFCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 324))

Abstract

During the last few years, unprecedented progress has been made in structural complexity theory; class inclusions and relativized separations were discovered, and hierarchies collapsed. We survey this progress, highlighting the central role of counting techniques. We also present a new result whose proof demonstrates the power of combinatorial arguments: there is a relativized world in which UP has no Turing complete sets.

Supported by NSF grant CCR-8809174 and a Hewlett-Packard Corporation equipment grant.

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Authors and Affiliations

  1. Department of Computer Science, Columbia University, 10027, New York, NY, USA

    Lane A. Hemachandra

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  1. Lane A. Hemachandra
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Michal P. Chytil Václav Koubek Ladislav Janiga

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© 1988 Springer-Verlag Berlin Heidelberg

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Hemachandra, L.A. (1988). Structure of complexity classes: Separations, collapses, and completeness. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017131

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  • DOI: https://doi.org/10.1007/BFb0017131

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  • Print ISBN: 978-3-540-50110-7

  • Online ISBN: 978-3-540-45926-2

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