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Superpolynomial circuits, almost sparse oracles and the exponential hierarchy

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 652))

Abstract

Several problems concerning superpolynomial size circuits and superpolynomial-time advice classes are investigated. First we consider the implications of NP (and other fundamental complexity classes) having circuits slighter bigger than polynomial. We prove that if such circuits exist, for example if NP has n logn size circuits, the exponential hierarchy collapses to the second level. Next we consider the consequences of the bottom levels of the exponential hierarchy being contained in small advice classes. Again various collapses result. For example, if EXP NP \(\subseteq\) EXP/poly then EXP NP =EXP.

This research was done while visiting the Boston University Computer Science Department with the support of NSF Grant CCR-8814339, The Netherlands Organization for Scientific research (NWO) grant SIR 13-603 and NWO-programma voor korte reisbeurzen.

Supported in part by National Science Foundation Grants CCR-8814339 and CCR-9103055.

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Authors and Affiliations

  1. Depts of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam

    Harry Buhrman

  2. Computer Science Department, Boston University, 02215, Boston, MA

    Steven Homer

Authors
  1. Harry Buhrman
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  2. Steven Homer
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Rudrapatna Shyamasundar

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© 1992 Springer-Verlag Berlin Heidelberg

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Buhrman, H., Homer, S. (1992). Superpolynomial circuits, almost sparse oracles and the exponential hierarchy. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_99

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  • DOI: https://doi.org/10.1007/3-540-56287-7_99

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56287-0

  • Online ISBN: 978-3-540-47507-1

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