Visibly Counter Languages and the Structure of \(\mathrm {NC}^{1}\)

  • Michael HahnEmail author
  • Andreas Krebs
  • Klaus-Jörn Lange
  • Michael Ludwig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)


We extend the familiar program of understanding circuit complexity in terms of regular languages to visibly counter languages. Like the regular languages, the visibly counter languages are \(\mathrm {NC}^{1}\)- complete. We investigate what the visibly counter languages in certain constant depth circuit complexity classes are. We have initiated this in a previous work for \(\mathrm {AC}^{0}\). We present characterizations and decidability results for various logics and circuit classes. In particular, our approach yields a way to understand \(\mathrm {TC}^{0}\), where the regular approach fails.


Word Problem Logic Class Regular Language Pushdown Automaton Nonsolvable Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

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

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