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A Logical Characterisation of Linear Time on Nondeterministic Turing Machines

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

The paper gives a logical characterisation of the class NTIME(n) of problems that can be solved on a nondeterministic Turing machine in linear time. It is shown that a set L of strings is in this class if and only if there is a formula of the form ∃f 1··∃f k ∃R 1··∃R m ∀xϕ that is true exactly for all strings in L. In this formula the f i are unary function symbols, the R i are unary relation symbols and ϕ is a quantifier-free formula. Furthermore, the quantification of functions is restricted to non-crossing, decreasing functions and in ϕ no equations in which different functions occur are allowed. There are a number of variations of this statement, e.g., it holds also for k = 3. From these results we derive an Ehrenfeucht game characterisation of NTIME(n).

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Author information

Authors and Affiliations

  1. Institut für Informatik / FB 17, Johannes Gutenberg-Universität, D-55099, Mainz

    Clemens Lautemann, Nicole Schweikardt & Thomas Schwentick

Authors
  1. Clemens Lautemann
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  2. Nicole Schweikardt
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  3. Thomas Schwentick
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Editor information

Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Lautemann, C., Schweikardt, N., Schwentick, T. (1999). A Logical Characterisation of Linear Time on Nondeterministic Turing Machines. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_13

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  • DOI: https://doi.org/10.1007/3-540-49116-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

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