Nearly linear time

  • Yuri Gurevich
  • Saharon Shelah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 363)


The notion of linear-time computability is very sensitive to machine model. In this connection, we introduce a class NLT of functions computable in nearly linear time n(log n)O(1) on random access computers. NLT is very robust and does not depend on the particular choice of random access computers. Kolmogorov machines, Schönhage machines, random access Turing machines, etc., also compute exactly NLT functions in nearly linear time. It is not known whether usual multitape Turing machines are able to compute all NLT functions in nearly linear time. We do not believe they are and do not consider them necessarily appropriate for this relatively low complexity level. It turns out, however, that nondeterministic Turing machines accept exactly the languages in the nondeterministic version of NLT. We give also a machine-independent definition of NLT and a natural problem complete for NLT.


Linear Time Turing Machine Binary String Machine Model Parameter String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Yuri Gurevich
    • 1
  • Saharon Shelah
    • 2
    • 3
  1. 1.Electrical Engineering and Computer ScienceUniversity of MichiganAnn Arbor
  2. 2.MathematicsHebrew UniversityJerusalemIsrael
  3. 3.MathematicsRutgers UniversityNew Brunswick

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