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International Conference on Developments in Language Theory

DLT 2002: Developments in Language Theory pp 185–196Cite as

A Space Lower Bound of Two-Dimensional Probabilistic Turing Machines

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

Abstract

This paper shows a sublogarithmic space lower bound for two-dimensional probabilistic Turing machines (2-ptm’s) over square tapes with bounded error, and shows, using this space lower bound theorem, that a specific set is not recognized by any o(log n) space-bounded 2- ptm. Furthermore, the paper investigates a relationship between 2-ptm's and two-dimensional Turing machines with both nondeterministic and probabilistic states, which we call “two-dimensional stochastic Turing machines (2-stm’s)”, and shows that for any loglog n ≤ L(n) = o(log n), L(n) space-bounded 2-ptm’s with bounded error are less powerful than L(n) space-bounded 2-stm’s with bounded error which start in nondeterministic mode, and make only one alternation between nondeterministic and probabilistic modes.

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Author information

Authors and Affiliations

  1. Chitose Factory, Hitachi Kokusai Electronocs, 066-8566, Chitose, Japan

    Yuji Sasaki

  2. Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, 755-8611, Ube, Japan

    Katsushi Inoue & Akira Ito

  3. Media and Information Technology Center, Yamaguchi University, 755-8611, Ube, Japan

    Yue Wang

Authors
  1. Yuji Sasaki
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  2. Katsushi Inoue
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  3. Akira Ito
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  4. Yue Wang
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Editor information

Editors and Affiliations

  1. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

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© 2003 Springer-Verlag Berlin Heidelberg

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Sasaki, Y., Inoue, K., Ito, A., Wang, Y. (2003). A Space Lower Bound of Two-Dimensional Probabilistic Turing Machines. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_16

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  • DOI: https://doi.org/10.1007/3-540-45005-X_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

  • eBook Packages: Springer Book Archive

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