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)


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).


Linear Time Turing Machine Derivation Tree Relational Atom Logical Characterisation 
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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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