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Expanders, randomness, or time versus space

extended abstract
  • Michael Sipser
Conference paper
Part of the Lecture Notes in Computer Science book series (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),
$$EH \to (P = R or (TIME(t(n)) \cap \{ 1\} * ) \subseteq io - SPACE(t^{1 - \varepsilon } (n))$$

Keywords

Error Probability Explicit Construction Expander Graph Unary Language Left Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Michael Sipser
    • 1
    • 2
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeley
  2. 2.Mathematics DepartmentMITCambridge

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