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International Symposium on Mathematical Foundations of Computer Science

MFCS 1995: Mathematical Foundations of Computer Science 1995 pp 159–168Cite as

Nonuniform lower bounds for exponential time classes

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 969))

Abstract

Lower bounds for the first levels of the exponential time hierarchy with respect to circuit and advice classes are studied. Using time bounded Kolmogorov complexity, languages are constructed which witness that various exponential time classes are not included in (fixed) polynomial advice classes. We show as well that these languages are not included in small circuit families where the circuits are of a fixed, polynomial size. The results yield optimal bounds (up to relativization) on efficient nonuniform computation.

Research partially supported by the National Science Foundation under grants CCR-9103055 and CCR-9400229.

Research partially supported by the National Science Foundation under grant CCR-9410713.

We thanks Jack Lutz for referring us to his previous work and pointing out the relationships to the results in Section 2.

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Author information

Authors and Affiliations

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

    Steven Homer

  2. Computer Science Department, Portland State University, 97207, Portland, Oregon

    Sarah Mocas

Authors
  1. Steven Homer
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  2. Sarah Mocas
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Jiří Wiedermann Petr Hájek

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© 1995 Springer-Verlag Berlin Heidelberg

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Homer, S., Mocas, S. (1995). Nonuniform lower bounds for exponential time classes. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_122

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  • DOI: https://doi.org/10.1007/3-540-60246-1_122

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60246-0

  • Online ISBN: 978-3-540-44768-9

  • eBook Packages: Springer Book Archive

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