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A Logical Characterisation of Linear Time on Nondeterministic Turing Machines

  • Clemens Lautemann
  • Nicole Schweikardt
  • Thomas Schwentick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1563)

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).

Keywords

Linear Time Turing Machine Derivation Tree Relational Atom Logical Characterisation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Clemens Lautemann
    • 1
  • Nicole Schweikardt
    • 1
  • Thomas Schwentick
    • 1
  1. 1.Institut für Informatik / FB 17Johannes Gutenberg-UniversitätMainz

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