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On alternation II

A graph theoretic approach to determinism versus nondeterminism

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Summary

Every deterministic t(n)-time bounded multitape Turing machine can be simulated by an alternating t(n) loglog t(n)/log t(n)-time bounded Turing machine.

If the depth of every directed acyclic graph with n edges can be reduced to log n by removing only o(n) edges, then in linear time nondeterministic multitape Turing machines can recognize mor languages than deterministic multitape Turing machines. For some graphs reduction of the depth to log n requires the removal of Ω(n/loglog n) edges. A graph theoretic condition is given, which implies that obliviousness reduces the power of multitape Turing machines.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 4800, Bielefeld 1, Germany (Fed. Rep.)

    Wolfgang Paul & Rüdiger Reischuk

Authors
  1. Wolfgang Paul
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  2. Rüdiger Reischuk
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Additional information

Part of this research was done while the author was visiting the ‘Laboratoire de recherches en informatique de l'université de Paris sud’ under DAAD-grant 311-f-HSLA-soe

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Paul, W., Reischuk, R. On alternation II. Acta Informatica 14, 391–403 (1980). https://doi.org/10.1007/BF00286494

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  • DOI: https://doi.org/10.1007/BF00286494

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