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International Symposium on Mathematical Foundations of Computer Science

MFCS 1997: Mathematical Foundations of Computer Science 1997 pp 91–107Cite as

Computational limitations of Stochastic Turing machines and Arthur-Merlin games with small space bounds

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1295))

Abstract

A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, Arthur-Merlin games, or interactive proof systems with public coins. We give an overview on complexity classes defined by STMs with space resources between constant and logarithmic size and constant or sublinear bounds on the number of alternations. New lower space bounds are shown for a specific family of languages by exploiting combinatorial properties. These results imply an infinite hierarchy with respect to the number of alternations of STMs, and nonclosure properties of certain classes.

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Author information

Authors and Affiliations

  1. Instytut Informatyki, Uniwersytet Wrocławski, 51-151, Wrocław, Poland

    Maciej Liśkiewicz

  2. Institut für Theoretische Informatik, Med. Universität zu Lübeck, D-23560, Lübeck, Germany

    Rüdiger Reischuk

Authors
  1. Maciej Liśkiewicz
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  2. Rüdiger Reischuk
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Editor information

Igor Prívara Peter Ružička

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© 1997 Springer-Verlag Berlin Heidelberg

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Liśkiewicz, M., Reischuk, R. (1997). Computational limitations of Stochastic Turing machines and Arthur-Merlin games with small space bounds. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029952

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  • DOI: https://doi.org/10.1007/BFb0029952

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63437-9

  • Online ISBN: 978-3-540-69547-9

  • eBook Packages: Springer Book Archive

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