On Distinguishing NC\(^1\) and NL

  • Andreas Krebs
  • Klaus-Jörn LangeEmail author
  • Michael Ludwig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


We obtain results within the area of dense completeness, which describes a close relation between families of formal languages and complexity classes. Previously we were able show that this relation exists between counter languages and \(\mathbf {NL}\) but not between the regular languages and \(\mathbf {NC^1}\).

We narrow the gap between the regular languages and the counter languages by considering visibly counter languages. It turns out that they are not densely complete for \(\mathbf {NC^1}\). At the same time we found a restricted counter automaton model which is densely complete for \(\mathbf {NL}\).

Besides counter automata we show more positive examples in terms of L-systems.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Andreas Krebs
    • 1
  • Klaus-Jörn Lange
    • 1
    Email author
  • Michael Ludwig
    • 1
  1. 1.WSI - University of TübingenTübingenGermany

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