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Improved time and space hierarchies of one-tape off-line TMs

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

This paper presents improved time and space hierarchies of one-tape off-line Turing Machines (TMs), which have a single worktape and a two-way input tape: (i) For any time-constructible functions t 1 (n) and t 2(n) such that infn→∞ t 1(n) log log t 1(n)/t 2(n) = 0 and t 1(n) = nO(1), there is a language which can be accepted by a t 2(n)-time TM, but not by any t 1(n)-time TM. (ii) For any space-constructible function s(n) and positive constant ε, there is a language which can be accepted in space s(n) + log s(n) + (2 + ε) log log s(n) by a TM with two worktape-symbols, but not in space s(n) by any TM with the same worktape-symbols. The (log log t 1(n))-gap in (i) substantially improves the Hartmanis and Stearns' (log t 1(n))-gap which survived more than 30 years.

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Author information

Authors and Affiliations

  1. Kyoto University, 606-8501, Kyoto, Japan

    Kazuo Iwama

  2. Hiroshima University, 739-8527, Higashi-Hiroshima, Japan

    Chuzo Iwamoto

Authors
  1. Kazuo Iwama
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  2. Chuzo Iwamoto
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Iwama, K., Iwamoto, C. (1998). Improved time and space hierarchies of one-tape off-line TMs. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055808

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  • DOI: https://doi.org/10.1007/BFb0055808

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

  • eBook Packages: Springer Book Archive

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