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Expanders, randomness, or time versus space

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Book cover Structure in Complexity Theory

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 223))

Abstract

Let EH be the hypothesis that a certain type of expander graph has an explicit construction. Let io-SPACE(T(n)) be the class of problems solvable by algorithms which for infinitely many inputs use at most space t(n). Then the following holds:

There exists ε>0 such that for any time bound t(n),

$$EH \to (P = R or (TIME(t(n)) \cap \{ 1\} * ) \subseteq io - SPACE(t^{1 - \varepsilon } (n))$$

Research supported in part by NSF Grant MCS-8304769 and Air Force Grant AFOSR-82-0326.

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References

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Authors and Affiliations

  1. Computer Science Division, University of California, 94720, Berkeley, CA

    Michael Sipser

  2. Mathematics Department, MIT, 02139, Cambridge, MA

    Michael Sipser

Authors
  1. Michael Sipser
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Alan L. Selman

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© 1986 Springer-Verlag Berlin Heidelberg

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Sipser, M. (1986). Expanders, randomness, or time versus space. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_108

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  • DOI: https://doi.org/10.1007/3-540-16486-3_108

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16486-9

  • Online ISBN: 978-3-540-39825-7

  • eBook Packages: Springer Book Archive

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